Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
550 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#66432 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×((C3⋊D3)⋊C3)⋊D3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10619893 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10619887 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#6200 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #6292⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #6289⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #88955 | — | 3 | 1 | no | maximal |
| 9 | #88954 | — | 3 | 1 | no | maximal |
| 10 | #88654 | — | 3 | 1 | no | maximal |
| 11 | C2×C3⋊#272 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×C3×#272 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C2×C3⋊((C3⋊D3)⋊C3) | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C3⋊((C3⋊D3)⋊C3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C2×C3×(C3⋊D3)⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #66432 | — | 2 | 2 | no | — |
| 17 | ((C3⋊D3)⋊C3)⋊D3 | — | 2 | 2 | no | — |
| 18 | Dic3×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C3×(C3⋊Dic3)⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C2×#1113 | — | 3 | 1 | no | — |
| 21 | C2×D3×C3⋊D3 | — | 3 | 1 | no | — |
| 22 | C2×D3×C3⋊D3 | — | 3 | 1 | no | — |
| 23 | C2×D3×C3⋊D3 | — | 3 | 1 | no | — |
| 24 | #6295 | — | 3 | 1 | no | — |
| 25 | #6292 | — | 3 | 1 | no | — |
| 26 | #6292 | D3 | 1 | 1 | yes | characteristic, complemented |
| 27 | #6289 | D3 | 1 | 1 | yes | characteristic, complemented |
| 28 | C3×#626 | — | 3 | 1 | no | — |
| 29 | C3×#626 | — | 3 | 1 | no | — |
| 30 | C3×#626 | — | 3 | 1 | no | — |
| 31 | C3×#626 | — | 3 | 1 | no | — |
| 32 | C3×#626 | — | 6 | 1 | no | — |
| 33 | C3×#625 | — | 3 | 1 | no | — |
| 34 | C3×#624 | — | 3 | 1 | no | — |
| 35 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 1 | no | — |
| 36 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 3 | 1 | no | — |
| 37 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 6 | 1 | no | — |
| 38 | C4⋊#272 | — | 3 | 1 | no | — |
| 39 | C4⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 40 | C4×(C3⋊D3)⋊C3 | — | 3 | 1 | no | — |
| 41 | #6200 | — | 3 | 1 | no | — |
| 42 | #6200 | — | 6 | 1 | no | — |
| 43 | #6200 | D3 | 1 | 1 | yes | characteristic, complemented |
| 44 | C2×C3×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 45 | C3⋊#272 | — | 2 | 1 | no | — |
| 46 | C3×#272 | — | 2 | 1 | no | — |
| 47 | C3⋊((C3⋊D3)⋊C3) | — | 2 | 1 | no | — |
| 48 | C3⋊((C3⋊D3)⋊C3) | D4 | 1 | 2 | yes | complemented |
| 49 | C3×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 50 | #3811 | — | 9 | 1 | no | — |
| 51 | #3811 | — | 9 | 1 | no | — |
| 52 | #3802 | — | 9 | 1 | no | — |
| 53 | D3×D12 | — | 9 | 1 | no | — |
| 54 | D3×D12 | — | 9 | 1 | no | — |
| 55 | C2×C3⋊(C3⋊D3) | C2×D3 | 1 | 1 | yes | characteristic |
| 56 | C2×C3⋊(C3⋊D3) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 57 | C2×C3×C3⋊D3 | — | 3 | 1 | no | — |
| 58 | C2×C3×C3⋊D3 | — | 3 | 1 | no | — |
| 59 | C2×C3×C3⋊D3 | — | 3 | 1 | no | — |
| 60 | C2×C3×C3⋊D3 | — | 3 | 1 | no | — |
| 61 | C2×C3×C3⋊D3 | — | 6 | 1 | no | — |
| 62 | C2×C3×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 63 | C2×C32×D3 | — | 3 | 1 | no | — |
| 64 | C2×C32×D3 | — | 3 | 1 | no | — |
| 65 | C2×C32×D3 | — | 3 | 1 | no | — |
| 66 | C2×C32×D3 | — | 6 | 1 | no | — |
| 67 | #1113 | — | 6 | 2 | no | — |
| 68 | D3×C3⋊D3 | — | 6 | 2 | no | — |
| 69 | D3×C3⋊D3 | — | 6 | 2 | no | — |
| 70 | D3×C3⋊D3 | — | 6 | 2 | no | — |
| 71 | C3×C3⋊Dic3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 72 | C32×Dic3 | — | 2 | 1 | no | — |
| 73 | C32×Dic3 | — | 3 | 1 | no | — |
| 74 | C32×Dic3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 75 | C32×Dic3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 76 | C2×#272 | — | 3 | 1 | no | — |
| 77 | C2×#272 | — | 6 | 1 | no | — |
| 78 | C2×#272 | — | 6 | 1 | no | — |
| 79 | C2×#272 | — | 12 | 1 | no | — |
| 80 | C2×#272 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 81 | C2×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 82 | C2×(C3⋊D3)⋊C3 | — | 3 | 1 | no | — |
| 83 | C2×(C3⋊D3)⋊C3 | — | 3 | 1 | no | — |
| 84 | C2×(C3⋊D3)⋊C3 | — | 6 | 1 | no | — |
| 85 | C2×(C3⋊D3)⋊C3 | — | 6 | 1 | no | — |
| 86 | C2×(C3⋊D3)⋊C3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 87 | ((C3⋊D3)⋊C3)⋊C2 | — | 6 | 2 | no | — |
| 88 | ((C3⋊D3)⋊C3)⋊C2 | — | 6 | 4 | no | — |
| 89 | ((C3⋊D3)⋊C3)⋊C2 | — | 6 | 2 | no | — |
| 90 | C4×H(3,𝔽3) | — | 3 | 1 | no | — |
| 91 | (C3⋊Dic3)⋊C3 | — | 2 | 1 | no | — |
| 92 | (C3⋊Dic3)⋊C3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 93 | C3×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 94 | C22×C3⋊D3 | — | 9 | 1 | no | — |
| 95 | C22×C3⋊D3 | — | 9 | 1 | no | — |
| 96 | C2×D32 | — | 9 | 1 | no | — |
| 97 | C2×D32 | — | 9 | 1 | no | — |
| 98 | C2×D32 | — | 9 | 1 | no | — |
| 99 | C2×D32 | — | 9 | 1 | no | — |
| 100 | C2×D32 | — | 9 | 1 | no | — |
| 101 | C2×D32 | — | 9 | 1 | no | — |
| 102 | C2×D32 | — | 9 | 1 | no | — |
| 103 | C2×D32 | — | 9 | 1 | no | — |
| 104 | C2×D32 | — | 18 | 1 | no | — |
| 105 | C2×D32 | — | 18 | 1 | no | — |
| 106 | C2×D32 | — | 18 | 1 | no | — |
| 107 | C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 108 | C4⋊(C3⋊D3) | — | 9 | 1 | no | — |
| 109 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 110 | C3×#67 | — | 9 | 1 | no | — |
| 111 | C3×#67 | — | 9 | 1 | no | — |
| 112 | C3×#67 | — | 9 | 1 | no | — |
| 113 | C3×#67 | — | 9 | 1 | no | — |
| 114 | C3×D12 | — | 9 | 1 | no | — |
| 115 | C3×D12 | — | 9 | 1 | no | — |
| 116 | C3×D12 | — | 9 | 1 | no | — |
| 117 | C3×D12 | — | 9 | 1 | no | — |
| 118 | C3×D12 | — | 18 | 1 | no | — |
| 119 | C3×C4×D3 | — | 9 | 1 | no | — |
| 120 | C3×C4×D3 | — | 9 | 1 | no | — |
| 121 | #626 | — | 3 | 1 | no | — |
| 122 | #626 | — | 3 | 1 | no | — |
| 123 | #626 | — | 3 | 1 | no | — |
| 124 | #626 | — | 3 | 1 | no | — |
| 125 | #626 | — | 6 | 1 | no | — |
| 126 | #626 | — | 9 | 1 | no | — |
| 127 | #626 | — | 9 | 1 | no | — |
| 128 | #626 | — | 9 | 1 | no | — |
| 129 | #626 | — | 9 | 1 | no | — |
| 130 | #626 | — | 18 | 1 | no | — |
| 131 | #625 | — | 3 | 1 | no | — |
| 132 | #625 | — | 9 | 1 | no | — |
| 133 | #624 | — | 3 | 1 | no | — |
| 134 | #624 | — | 9 | 1 | no | — |
| 135 | C2×C33 | — | 2 | 1 | no | — |
| 136 | C2×C33 | C22×D3 | 1 | 1 | yes | characteristic |
| 137 | C2×C33 | C22×D3 | 1 | 1 | yes | characteristic |
| 138 | C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 139 | C3⋊(C3⋊D3) | D12 | 1 | 2 | yes | complemented |
| 140 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 141 | C3×C3⋊D3 | — | 3 | 2 | no | — |
| 142 | C3×C3⋊D3 | — | 6 | 1 | no | — |
| 143 | C3×C3⋊D3 | — | 6 | 1 | no | — |
| 144 | C3×C3⋊D3 | — | 6 | 1 | no | — |
| 145 | C3×C3⋊D3 | — | 12 | 1 | no | — |
| 146 | C32×D3 | — | 6 | 1 | no | — |
| 147 | C32×D3 | — | 6 | 1 | no | — |
| 148 | C32×D3 | — | 6 | 1 | no | — |
| 149 | C32×D3 | — | 12 | 1 | no | — |
| 150 | C2×H(3,𝔽3) | — | 2 | 1 | no | — |
| 151 | C2×H(3,𝔽3) | — | 2 | 1 | no | — |
| 152 | C2×H(3,𝔽3) | — | 4 | 1 | no | — |
| 153 | C2×H(3,𝔽3) | C22×D3 | 1 | 1 | yes | characteristic |
| 154 | #272 | — | 2 | 1 | no | — |
| 155 | #272 | — | 6 | 2 | no | — |
| 156 | #272 | — | 6 | 1 | no | — |
| 157 | #272 | — | 12 | 1 | no | — |
| 158 | #272 | — | 12 | 2 | no | — |
| 159 | (C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 160 | (C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 161 | (C3⋊D3)⋊C3 | — | 3 | 2 | no | — |
| 162 | (C3⋊D3)⋊C3 | — | 6 | 2 | no | — |
| 163 | (C3⋊D3)⋊C3 | — | 6 | 1 | no | — |
| 164 | (C3⋊D3)⋊C3 | — | 12 | 1 | no | — |
| 165 | D3×D4 | — | 27 | 1 | no | — |
| 166 | D3×D4 | — | 27 | 1 | no | — |
| 167 | D3×D4 | — | 27 | 1 | no | — |
| 168 | C2×D12 | — | 27 | 1 | no | — |
| 169 | C22×C32 | — | 9 | 1 | no | — |
| 170 | C22×C32 | — | 9 | 1 | no | — |
| 171 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 172 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 173 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 174 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 175 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 176 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 177 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 178 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 179 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 180 | C2×C3⋊D3 | — | 9 | 1 | no | — |
| 181 | C2×C3⋊D3 | — | 9 | 1 | no | — |
| 182 | C2×C3⋊D3 | — | 18 | 1 | no | — |
| 183 | C2×C3⋊D3 | — | 18 | 1 | no | — |
| 184 | C2×C3⋊D3 | — | 18 | 2 | no | — |
| 185 | C2×C3⋊D3 | — | 18 | 2 | no | — |
| 186 | C2×C3⋊D3 | D32 | 1 | 1 | yes | characteristic, complemented |
| 187 | C2×C3×D3 | — | 3 | 1 | no | — |
| 188 | C2×C3×D3 | — | 3 | 1 | no | — |
| 189 | C2×C3×D3 | — | 3 | 1 | no | — |
| 190 | C2×C3×D3 | — | 3 | 1 | no | — |
| 191 | C2×C3×D3 | — | 3 | 1 | no | — |
| 192 | C2×C3×D3 | — | 3 | 1 | no | — |
| 193 | C2×C3×D3 | — | 6 | 1 | no | — |
| 194 | C2×C3×D3 | — | 6 | 1 | no | — |
| 195 | C2×C3×D3 | — | 6 | 1 | no | — |
| 196 | C2×C3×D3 | — | 6 | 1 | no | — |
| 197 | C2×C3×D3 | — | 6 | 1 | no | — |
| 198 | C2×C3×D3 | — | 9 | 1 | no | — |
| 199 | C2×C3×D3 | — | 9 | 1 | no | — |
| 200 | C2×C3×D3 | — | 9 | 1 | no | — |
| 201 | C2×C3×D3 | — | 9 | 1 | no | — |
| 202 | C2×C3×D3 | — | 9 | 1 | no | — |
| 203 | C2×C3×D3 | — | 9 | 1 | no | — |
| 204 | C2×C3×D3 | — | 9 | 1 | no | — |
| 205 | C2×C3×D3 | — | 9 | 1 | no | — |
| 206 | C2×C3×D3 | — | 12 | 1 | no | — |
| 207 | C2×C3×D3 | — | 18 | 1 | no | — |
| 208 | C2×C3×D3 | — | 18 | 1 | no | — |
| 209 | C2×C3×D3 | — | 18 | 1 | no | — |
| 210 | C2×C3×D3 | — | 18 | 1 | no | — |
| 211 | C2×C3×D3 | — | 18 | 1 | no | — |
| 212 | C2×C3×D3 | — | 36 | 1 | no | — |
| 213 | D32 | — | 18 | 2 | no | — |
| 214 | D32 | — | 18 | 2 | no | — |
| 215 | D32 | — | 18 | 2 | no | — |
| 216 | D32 | — | 18 | 2 | no | — |
| 217 | D32 | — | 18 | 2 | no | — |
| 218 | D32 | — | 18 | 4 | no | — |
| 219 | D32 | — | 18 | 2 | no | — |
| 220 | D32 | — | 18 | 4 | no | — |
| 221 | D32 | — | 18 | 4 | no | — |
| 222 | D32 | — | 18 | 2 | no | — |
| 223 | D32 | — | 18 | 2 | no | — |
| 224 | C32×C4 | — | 3 | 1 | no | — |
| 225 | C32×C4 | — | 3 | 1 | no | — |
| 226 | C32×C4 | — | 6 | 1 | no | — |
| 227 | C32×C4 | — | 9 | 1 | no | — |
| 228 | C3⋊Dic3 | D32 | 1 | 1 | yes | characteristic, complemented |
| 229 | C3×Dic3 | — | 3 | 1 | no | — |
| 230 | C3×Dic3 | — | 3 | 1 | no | — |
| 231 | C3×Dic3 | — | 3 | 1 | no | — |
| 232 | C3×Dic3 | — | 3 | 1 | no | — |
| 233 | C3×Dic3 | — | 6 | 1 | no | — |
| 234 | C3×Dic3 | — | 6 | 1 | no | — |
| 235 | C3×Dic3 | — | 9 | 1 | no | — |
| 236 | C3×Dic3 | D32 | 1 | 1 | yes | characteristic |
| 237 | C33 | — | 2 | 1 | no | — |
| 238 | C33 | C2×D12 | 1 | 1 | yes | characteristic, complemented |
| 239 | C33 | D3×D4 | 1 | 1 | yes | characteristic, complemented |
| 240 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 241 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 242 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 243 | H(3,𝔽3) | D3×D4 | 1 | 1 | yes | characteristic, complemented |
| 244 | C22×D3 | — | 27 | 1 | no | — |
| 245 | C22×D3 | — | 27 | 1 | no | — |
| 246 | C22×D3 | — | 27 | 1 | no | — |
| 247 | C22×D3 | — | 27 | 1 | no | — |
| 248 | C22×D3 | — | 27 | 1 | no | — |
| 249 | C22×D3 | — | 27 | 1 | no | — |
| 250 | C22×D3 | — | 27 | 1 | no | — |
| 251 | C22×D3 | — | 27 | 1 | no | — |
| 252 | C22×D3 | — | 54 | 1 | no | — |
| 253 | C22×D3 | — | 54 | 1 | no | — |
| 254 | C3×D4 | — | 27 | 1 | no | — |
| 255 | C3×D4 | — | 27 | 1 | no | — |
| 256 | C3×D4 | — | 27 | 1 | no | — |
| 257 | C2×C3×C4 | — | 27 | 1 | no | — |
| 258 | #67 | — | 9 | 1 | no | — |
| 259 | #67 | — | 9 | 1 | no | — |
| 260 | #67 | — | 9 | 1 | no | — |
| 261 | #67 | — | 9 | 1 | no | — |
| 262 | #67 | — | 27 | 1 | no | — |
| 263 | #67 | — | 27 | 1 | no | — |
| 264 | D12 | — | 9 | 1 | no | — |
| 265 | D12 | — | 9 | 1 | no | — |
| 266 | D12 | — | 9 | 1 | no | — |
| 267 | D12 | — | 9 | 1 | no | — |
| 268 | D12 | — | 18 | 1 | no | — |
| 269 | D12 | — | 27 | 1 | no | — |
| 270 | D12 | — | 27 | 1 | no | — |
| 271 | D12 | — | 27 | 1 | no | — |
| 272 | D12 | — | 54 | 1 | no | — |
| 273 | C4×D3 | — | 9 | 1 | no | — |
| 274 | C4×D3 | — | 9 | 1 | no | — |
| 275 | C4×D3 | — | 27 | 1 | no | — |
| 276 | C2×C32 | — | 2 | 1 | no | — |
| 277 | C2×C32 | — | 2 | 1 | no | — |
| 278 | C2×C32 | — | 2 | 1 | no | — |
| 279 | C2×C32 | — | 3 | 1 | no | — |
| 280 | C2×C32 | — | 3 | 1 | no | — |
| 281 | C2×C32 | — | 4 | 1 | no | — |
| 282 | C2×C32 | — | 6 | 1 | no | — |
| 283 | C2×C32 | — | 6 | 1 | no | — |
| 284 | C2×C32 | — | 6 | 1 | no | — |
| 285 | C2×C32 | — | 12 | 1 | no | — |
| 286 | C2×C32 | — | 18 | 1 | no | — |
| 287 | C2×C32 | — | 18 | 1 | no | — |
| 288 | C2×C32 | C2×D32 | 1 | 1 | yes | characteristic |
| 289 | C2×C32 | C2×D32 | 1 | 1 | yes | characteristic |
| 290 | C2×C32 | C2×D32 | 1 | 1 | yes | characteristic |
| 291 | C3⋊D3 | — | 2 | 1 | no | — |
| 292 | C3⋊D3 | — | 3 | 2 | no | — |
| 293 | C3⋊D3 | — | 3 | 2 | no | — |
| 294 | C3⋊D3 | — | 6 | 2 | no | — |
| 295 | C3⋊D3 | — | 6 | 1 | no | — |
| 296 | C3⋊D3 | — | 6 | 1 | no | — |
| 297 | C3⋊D3 | — | 6 | 1 | no | — |
| 298 | C3⋊D3 | — | 6 | 1 | no | — |
| 299 | C3⋊D3 | — | 9 | 2 | no | — |
| 300 | C3⋊D3 | — | 12 | 1 | no | — |
| 301 | C3⋊D3 | — | 12 | 1 | no | — |
| 302 | C3⋊D3 | — | 18 | 2 | no | — |
| 303 | C3⋊D3 | — | 18 | 1 | no | — |
| 304 | C3⋊D3 | — | 18 | 2 | no | — |
| 305 | C3×D3 | — | 6 | 2 | no | — |
| 306 | C3×D3 | — | 6 | 1 | no | — |
| 307 | C3×D3 | — | 6 | 1 | no | — |
| 308 | C3×D3 | — | 6 | 2 | no | — |
| 309 | C3×D3 | — | 6 | 2 | no | — |
| 310 | C3×D3 | — | 6 | 1 | no | — |
| 311 | C3×D3 | — | 6 | 1 | no | — |
| 312 | C3×D3 | — | 6 | 1 | no | — |
| 313 | C3×D3 | — | 6 | 1 | no | — |
| 314 | C3×D3 | — | 9 | 2 | no | — |
| 315 | C3×D3 | — | 9 | 2 | no | — |
| 316 | C3×D3 | — | 12 | 1 | no | — |
| 317 | C3×D3 | — | 12 | 1 | no | — |
| 318 | C3×D3 | — | 12 | 2 | no | — |
| 319 | C3×D3 | — | 18 | 1 | no | — |
| 320 | C3×D3 | — | 18 | 2 | no | — |
| 321 | C3×D3 | — | 18 | 2 | no | — |
| 322 | C3×D3 | — | 18 | 1 | no | — |
| 323 | C3×D3 | — | 18 | 2 | no | — |
| 324 | C3×D3 | — | 18 | 1 | no | — |
| 325 | C3×D3 | — | 18 | 1 | no | — |
| 326 | C3×D3 | — | 18 | 1 | no | — |
| 327 | C3×D3 | — | 18 | 1 | no | — |
| 328 | C3×D3 | — | 36 | 1 | no | — |
| 329 | C3×D3 | — | 36 | 1 | no | — |
| 330 | C3×D3 | — | 36 | 2 | no | — |
| 331 | C2×D4 | — | 81 | 1 | no | Sylow |
| 332 | C22×C3 | — | 9 | 1 | no | — |
| 333 | C22×C3 | — | 9 | 1 | no | — |
| 334 | C22×C3 | — | 9 | 1 | no | — |
| 335 | C22×C3 | — | 9 | 1 | no | — |
| 336 | C22×C3 | — | 18 | 1 | no | — |
| 337 | C22×C3 | — | 18 | 1 | no | — |
| 338 | C22×C3 | — | 27 | 1 | no | — |
| 339 | C22×C3 | — | 27 | 1 | no | — |
| 340 | C22×C3 | — | 27 | 1 | no | — |
| 341 | C2×D3 | — | 3 | 1 | no | — |
| 342 | C2×D3 | — | 3 | 1 | no | — |
| 343 | C2×D3 | — | 3 | 1 | no | — |
| 344 | C2×D3 | — | 6 | 1 | no | — |
| 345 | C2×D3 | — | 9 | 1 | no | — |
| 346 | C2×D3 | — | 9 | 1 | no | — |
| 347 | C2×D3 | — | 9 | 1 | no | — |
| 348 | C2×D3 | — | 9 | 1 | no | — |
| 349 | C2×D3 | — | 9 | 1 | no | — |
| 350 | C2×D3 | — | 9 | 1 | no | — |
| 351 | C2×D3 | — | 9 | 1 | no | — |
| 352 | C2×D3 | — | 9 | 1 | no | — |
| 353 | C2×D3 | — | 18 | 1 | no | — |
| 354 | C2×D3 | — | 18 | 1 | no | — |
| 355 | C2×D3 | — | 18 | 1 | no | — |
| 356 | C2×D3 | — | 18 | 1 | no | — |
| 357 | C2×D3 | — | 18 | 1 | no | — |
| 358 | C2×D3 | — | 27 | 1 | no | — |
| 359 | C2×D3 | — | 27 | 1 | no | — |
| 360 | C2×D3 | — | 36 | 1 | no | — |
| 361 | C2×D3 | — | 54 | 1 | no | — |
| 362 | C2×D3 | — | 54 | 1 | no | — |
| 363 | C2×D3 | — | 54 | 2 | no | — |
| 364 | C2×D3 | — | 54 | 2 | no | — |
| 365 | C2×D3 | — | 54 | 2 | no | — |
| 366 | C2×D3 | — | 54 | 2 | no | — |
| 367 | C2×D3 | — | 54 | 2 | no | — |
| 368 | C2×D3 | — | 54 | 2 | no | — |
| 369 | C2×D3 | — | 54 | 4 | no | — |
| 370 | C2×D3 | — | 54 | 2 | no | — |
| 371 | C2×D3 | — | 54 | 2 | no | — |
| 372 | C2×D3 | — | 54 | 4 | no | — |
| 373 | C3×C4 | — | 3 | 1 | no | — |
| 374 | C3×C4 | — | 9 | 1 | no | — |
| 375 | C3×C4 | — | 9 | 1 | no | — |
| 376 | C3×C4 | — | 9 | 1 | no | — |
| 377 | C3×C4 | — | 9 | 1 | no | — |
| 378 | C3×C4 | — | 18 | 1 | no | — |
| 379 | C3×C4 | — | 18 | 1 | no | — |
| 380 | Dic3 | — | 3 | 1 | no | — |
| 381 | Dic3 | — | 9 | 1 | no | — |
| 382 | Dic3 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 383 | C32 | — | 2 | 1 | no | — |
| 384 | C32 | — | 2 | 1 | no | — |
| 385 | C32 | — | 2 | 1 | no | — |
| 386 | C32 | — | 3 | 1 | no | — |
| 387 | C32 | — | 3 | 1 | no | — |
| 388 | C32 | — | 4 | 1 | no | — |
| 389 | C32 | — | 6 | 1 | no | — |
| 390 | C32 | — | 6 | 1 | no | — |
| 391 | C32 | — | 6 | 1 | no | — |
| 392 | C32 | — | 12 | 1 | no | — |
| 393 | C32 | D3×D12 | 1 | 1 | yes | characteristic |
| 394 | C32 | D3×D12 | 1 | 1 | yes | characteristic, complemented |
| 395 | C32 | #3811 | 1 | 1 | yes | characteristic, complemented |
| 396 | C23 | — | 81 | 1 | no | — |
| 397 | C23 | — | 81 | 1 | no | — |
| 398 | D4 | — | 27 | 1 | no | — |
| 399 | D4 | — | 27 | 1 | no | — |
| 400 | D4 | — | 27 | 1 | no | — |
| 401 | D4 | — | 81 | 1 | no | — |
| 402 | C2×C4 | — | 27 | 1 | no | — |
| 403 | C2×C3 | — | 2 | 1 | no | — |
| 404 | C2×C3 | — | 3 | 1 | no | — |
| 405 | C2×C3 | — | 3 | 1 | no | — |
| 406 | C2×C3 | — | 6 | 1 | no | — |
| 407 | C2×C3 | — | 6 | 1 | no | — |
| 408 | C2×C3 | — | 6 | 1 | no | — |
| 409 | C2×C3 | — | 12 | 1 | no | — |
| 410 | C2×C3 | — | 18 | 2 | no | — |
| 411 | C2×C3 | — | 18 | 1 | no | — |
| 412 | C2×C3 | — | 18 | 2 | no | — |
| 413 | C2×C3 | — | 18 | 1 | no | — |
| 414 | C2×C3 | — | 18 | 1 | no | — |
| 415 | C2×C3 | — | 18 | 1 | no | — |
| 416 | C2×C3 | — | 27 | 2 | no | — |
| 417 | C2×C3 | — | 54 | 1 | no | — |
| 418 | C2×C3 | — | 54 | 1 | no | — |
| 419 | C2×C3 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 420 | C2×C3 | D33 | 1 | 1 | yes | characteristic |
| 421 | D3 | — | 6 | 1 | no | — |
| 422 | D3 | — | 6 | 1 | no | — |
| 423 | D3 | — | 6 | 1 | no | — |
| 424 | D3 | — | 9 | 2 | no | — |
| 425 | D3 | — | 9 | 2 | no | — |
| 426 | D3 | — | 12 | 1 | no | — |
| 427 | D3 | — | 18 | 1 | no | — |
| 428 | D3 | — | 18 | 2 | no | — |
| 429 | D3 | — | 18 | 2 | no | — |
| 430 | D3 | — | 18 | 1 | no | — |
| 431 | D3 | — | 18 | 1 | no | — |
| 432 | D3 | — | 18 | 2 | no | — |
| 433 | D3 | — | 18 | 1 | no | — |
| 434 | D3 | — | 18 | 1 | no | — |
| 435 | D3 | — | 18 | 1 | no | — |
| 436 | D3 | — | 27 | 2 | no | — |
| 437 | D3 | — | 36 | 1 | no | — |
| 438 | D3 | — | 36 | 1 | no | — |
| 439 | D3 | — | 36 | 2 | no | — |
| 440 | D3 | — | 54 | 2 | no | — |
| 441 | D3 | — | 54 | 1 | no | — |
| 442 | D3 | — | 108 | 1 | no | — |
| 443 | C22 | — | 9 | 1 | no | — |
| 444 | C22 | — | 9 | 1 | no | — |
| 445 | C22 | — | 27 | 1 | no | — |
| 446 | C22 | — | 27 | 1 | no | — |
| 447 | C22 | — | 27 | 1 | no | — |
| 448 | C22 | — | 162 | 2 | no | — |
| 449 | C22 | — | 162 | 2 | no | — |
| 450 | C4 | — | 3 | 1 | no | — |
| 451 | C4 | — | 9 | 1 | no | — |
| 452 | C3 | — | 2 | 1 | no | — |
| 453 | C3 | — | 3 | 1 | no | — |
| 454 | C3 | — | 3 | 1 | no | — |
| 455 | C3 | — | 6 | 1 | no | — |
| 456 | C3 | — | 6 | 1 | no | — |
| 457 | C3 | — | 6 | 1 | no | — |
| 458 | C3 | — | 12 | 1 | no | — |
| 459 | C3 | #88654 | 1 | 1 | yes | characteristic, complemented |
| 460 | C3 | #88955 | 1 | 1 | yes | characteristic |
| 461 | C2 | — | 18 | 1 | no | — |
| 462 | C2 | — | 18 | 1 | no | — |
| 463 | C2 | — | 27 | 2 | no | — |
| 464 | C2 | — | 54 | 1 | no | — |
| 465 | C2 | — | 54 | 1 | no | — |
| 466 | C2 | D3×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×((C3⋊D3)⋊C3)⋊C2 |
| commutator, Fitting, cosocle | C2×C3×H(3,𝔽3) | C23 |
| Frattini | C2×C3 | D33 |
| socle | C2×C32 | C2×D32 |
| hypocenter | C3×H(3,𝔽3) | C2×D4 |
| LCS | G ▷ C2×C3×H(3,𝔽3) ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#66432 | C2 | semidirect |
| 2. C2×((C3⋊D3)⋊C3)⋊D3 | C2 | semidirect |
| 3. #10619893 | C2 | semidirect |
| 4. #10619887 | C2 | semidirect |
| 5. C3×#6200 | C2 | semidirect |
| 6. #6292⋊C3 | C2 | semidirect |
| 7. #6289⋊C3 | C2 | semidirect |
| 11. C2×C3⋊#272 | C22 | semidirect |
| 12. C2×C3×#272 | C22 | semidirect |
| 14. C2×C3⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 15. C2×C3×(C3⋊D3)⋊C3 | C22 | semidirect |
| 18. Dic3×H(3,𝔽3) | C22 | semidirect |
| 19. C3×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 26. #6292 | D3 | semidirect |
| 27. #6289 | D3 | semidirect |
| 43. #6200 | D3 | semidirect |
| 48. C3⋊((C3⋊D3)⋊C3) | D4 | semidirect |
| 56. C2×C3⋊(C3⋊D3) | C2×D3 | semidirect |
| 62. C2×C3×C3⋊D3 | C2×D3 | semidirect |
| 71. C3×C3⋊Dic3 | C2×D3 | semidirect |
| 74. C32×Dic3 | C2×D3 | semidirect |
| 75. C32×Dic3 | C2×D3 | semidirect |
| 80. C2×#272 | C2×D3 | semidirect |
| 86. C2×(C3⋊D3)⋊C3 | C2×D3 | semidirect |
| 92. (C3⋊Dic3)⋊C3 | C2×D3 | semidirect |
| 93. C3×H(3,𝔽3) | C2×D4 | semidirect |
| 139. C3⋊(C3⋊D3) | D12 | semidirect |
| 186. C2×C3⋊D3 | D32 | semidirect |
| 228. C3⋊Dic3 | D32 | semidirect |
| 238. C33 | C2×D12 | semidirect |
| 239. C33 | D3×D4 | semidirect |
| 243. H(3,𝔽3) | D3×D4 | semidirect |
| 382. Dic3 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 394. C32 | D3×D12 | semidirect |
| 395. C32 | #3811 | semidirect |
| 459. C3 | #88654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66432 | 2 |
| C2×((C3⋊D3)⋊C3)⋊D3 | 2 |
| #10619893 | 2 |
| #10619887 | 2 |
| C3×#6200 | 2 |
| #6292⋊C3 | 2 |
| #6289⋊C3 | 2 |
| #88955 | 3 |
| #88954 | 3 |
| #88654 | 3 |