Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
773 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 773 conjugacy classes of subgroups — too many to draw. Only its 29 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 | (C3⋊D3)⋊(C22⋊A4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #120⋊H(3,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11720769 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3⋊D3×#120 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | D3×#120⋊C3 | — | 3 | 1 | no | maximal |
| 6 | C32⋊(C22⋊A4) | C22 | 1 | 1 | yes | characteristic, complemented |
| 7 | C2×(C3⋊D3)⋊A4 | — | 4 | 1 | no | maximal |
| 8 | C24×C3⋊D3 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 9 | D3×C22⋊A4 | — | 3 | 1 | no | — |
| 10 | C2×D4×C3⋊D3 | — | 3 | 1 | no | — |
| 11 | C32×#120 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 12 | #64162 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 13 | #64146 | — | 3 | 1 | no | — |
| 14 | #64091 | — | 3 | 1 | no | — |
| 15 | C22⋊C4×C3⋊D3 | — | 3 | 1 | no | — |
| 16 | C3×#120⋊C3 | — | 2 | 1 | no | — |
| 17 | C3×#120⋊C3 | D3 | 1 | 1 | yes | characteristic, complemented |
| 18 | C3⋊(#120⋊C3) | — | 3 | 1 | no | — |
| 19 | C2×C22⋊H(3,𝔽3) | — | 4 | 1 | no | — |
| 20 | (C3⋊D3)⋊A4 | — | 4 | 1 | no | — |
| 21 | (C3⋊D3)⋊A4 | — | 4 | 1 | no | — |
| 22 | (C3⋊D3)⋊A4 | — | 8 | 2 | no | — |
| 23 | D3×#120 | — | 3 | 1 | no | — |
| 24 | D3×#120 | — | 9 | 1 | no | — |
| 25 | C2×#120⋊C3 | — | 9 | 1 | no | — |
| 26 | C24×C32 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 27 | C23×C3⋊D3 | — | 3 | 1 | no | — |
| 28 | C23×C3⋊D3 | — | 3 | 1 | no | — |
| 29 | C23×C3⋊D3 | — | 6 | 2 | no | — |
| 30 | C23×C3⋊D3 | — | 6 | 2 | no | — |
| 31 | C23×C3⋊D3 | A4 | 1 | 1 | yes | characteristic, complemented |
| 32 | C3×C22⋊A4 | — | 2 | 1 | no | — |
| 33 | C3×C22⋊A4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 34 | C2×D3×A4 | — | 12 | 1 | no | — |
| 35 | C2×C32×D4 | — | 3 | 1 | no | — |
| 36 | C2×#638 | — | 3 | 1 | no | — |
| 37 | C2×#638 | — | 3 | 1 | no | — |
| 38 | D4×C3⋊D3 | — | 6 | 2 | no | — |
| 39 | D4×C3⋊D3 | — | 6 | 2 | no | — |
| 40 | C2×C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 41 | C2×C4×C3⋊D3 | — | 3 | 1 | no | — |
| 42 | C32×C22⋊C4 | — | 3 | 1 | no | — |
| 43 | #3757 | — | 3 | 1 | no | — |
| 44 | #3752 | — | 3 | 2 | no | — |
| 45 | C2×(C3⋊D3)⋊C3 | — | 16 | 1 | no | — |
| 46 | C22⋊H(3,𝔽3) | — | 4 | 1 | no | — |
| 47 | C22⋊H(3,𝔽3) | — | 8 | 2 | no | — |
| 48 | C24×D3 | — | 3 | 1 | no | — |
| 49 | C24×D3 | — | 9 | 1 | no | — |
| 50 | C2×C22⋊A4 | — | 9 | 1 | no | — |
| 51 | C2×D3×D4 | — | 9 | 1 | no | — |
| 52 | C2×D3×D4 | — | 9 | 3 | no | — |
| 53 | C3×#120 | — | 3 | 1 | no | — |
| 54 | C3×#120 | C3×D3 | 1 | 1 | yes | characteristic |
| 55 | #953 | — | 3 | 1 | no | — |
| 56 | #953 | — | 9 | 1 | no | — |
| 57 | #937 | — | 9 | 3 | no | — |
| 58 | #937 | — | 9 | 1 | no | — |
| 59 | #882 | — | 9 | 3 | no | — |
| 60 | #882 | — | 9 | 1 | no | — |
| 61 | D3×C22⋊C4 | — | 9 | 3 | no | — |
| 62 | D3×C22⋊C4 | — | 9 | 1 | no | — |
| 63 | #120⋊C3 | — | 3 | 1 | no | — |
| 64 | #120⋊C3 | — | 6 | 1 | no | — |
| 65 | #120⋊C3 | — | 9 | 1 | no | — |
| 66 | C23×C32 | — | 3 | 1 | no | — |
| 67 | C23×C32 | — | 6 | 2 | no | — |
| 68 | C23×C32 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 69 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 70 | C22×C3⋊D3 | — | 3 | 2 | no | — |
| 71 | C22×C3⋊D3 | — | 3 | 2 | no | — |
| 72 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 73 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 74 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 75 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 76 | C22×C3⋊D3 | — | 6 | 4 | no | — |
| 77 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 78 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 79 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 80 | C22×C3⋊D3 | — | 6 | 4 | no | — |
| 81 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 82 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 83 | C22×C3⋊D3 | C2×A4 | 1 | 1 | yes | characteristic |
| 84 | C22×C3⋊D3 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 85 | C2×C3×A4 | — | 4 | 1 | no | — |
| 86 | C2×C3×A4 | — | 8 | 1 | no | — |
| 87 | D3×A4 | — | 12 | 1 | no | — |
| 88 | D3×A4 | — | 12 | 1 | no | — |
| 89 | D3×A4 | — | 24 | 2 | no | — |
| 90 | C32×D4 | — | 6 | 2 | no | — |
| 91 | C2×C32×C4 | — | 3 | 1 | no | — |
| 92 | #638 | — | 6 | 2 | no | — |
| 93 | #638 | — | 6 | 2 | no | — |
| 94 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 95 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 96 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 97 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 98 | C2×#120 | — | 9 | 1 | no | Sylow |
| 99 | C2×H(3,𝔽3) | — | 16 | 1 | no | — |
| 100 | (C3⋊D3)⋊C3 | — | 16 | 1 | no | — |
| 101 | (C3⋊D3)⋊C3 | — | 16 | 1 | no | — |
| 102 | C24×C3 | — | 3 | 1 | no | — |
| 103 | C24×C3 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 104 | C23×D3 | — | 3 | 1 | no | — |
| 105 | C23×D3 | — | 9 | 1 | no | — |
| 106 | C23×D3 | — | 9 | 1 | no | — |
| 107 | C23×D3 | — | 9 | 3 | no | — |
| 108 | C23×D3 | — | 9 | 3 | no | — |
| 109 | C23×D3 | — | 9 | 1 | no | — |
| 110 | C23×D3 | — | 18 | 2 | no | — |
| 111 | C23×D3 | — | 18 | 6 | no | — |
| 112 | C23×D3 | — | 18 | 6 | no | — |
| 113 | C23×D3 | — | 18 | 2 | no | — |
| 114 | C22⋊A4 | — | 3 | 1 | no | — |
| 115 | C22⋊A4 | — | 6 | 1 | no | — |
| 116 | C22×A4 | — | 36 | 1 | no | — |
| 117 | C2×C3×D4 | — | 3 | 3 | no | — |
| 118 | C2×C3×D4 | — | 3 | 1 | no | — |
| 119 | C2×#67 | — | 9 | 1 | no | — |
| 120 | C2×#67 | — | 9 | 3 | no | — |
| 121 | C2×#67 | — | 9 | 3 | no | — |
| 122 | C2×#67 | — | 9 | 1 | no | — |
| 123 | D3×D4 | — | 18 | 2 | no | — |
| 124 | D3×D4 | — | 18 | 6 | no | — |
| 125 | D3×D4 | — | 18 | 6 | no | — |
| 126 | D3×D4 | — | 18 | 2 | no | — |
| 127 | C2×D12 | — | 9 | 1 | no | — |
| 128 | C2×D12 | — | 9 | 3 | no | — |
| 129 | C2×C4×D3 | — | 9 | 1 | no | — |
| 130 | C2×C4×D3 | — | 9 | 3 | no | — |
| 131 | C3×C22⋊C4 | — | 3 | 3 | no | — |
| 132 | C3×C22⋊C4 | — | 3 | 1 | no | — |
| 133 | #217 | — | 9 | 3 | no | — |
| 134 | #217 | — | 9 | 1 | no | — |
| 135 | (C2×D3)⋊C4 | — | 9 | 6 | no | — |
| 136 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 137 | C22×C32 | — | 2 | 2 | no | — |
| 138 | C22×C32 | — | 3 | 2 | no | — |
| 139 | C22×C32 | — | 6 | 1 | no | — |
| 140 | C22×C32 | — | 6 | 2 | no | — |
| 141 | C22×C32 | — | 6 | 2 | no | — |
| 142 | C22×C32 | C22×A4 | 1 | 1 | yes | characteristic |
| 143 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 144 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 145 | C2×C3⋊D3 | — | 3 | 2 | no | — |
| 146 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 147 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 148 | C2×C3⋊D3 | — | 6 | 4 | no | — |
| 149 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 150 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 151 | C2×C3⋊D3 | — | 6 | 4 | no | — |
| 152 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 153 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 154 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 155 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 156 | C2×C3×D3 | — | 48 | 1 | no | — |
| 157 | C3×A4 | — | 4 | 1 | no | — |
| 158 | C3×A4 | — | 8 | 2 | no | — |
| 159 | C3×A4 | — | 8 | 1 | no | — |
| 160 | C3×A4 | — | 16 | 2 | no | — |
| 161 | C32×C4 | — | 6 | 1 | no | — |
| 162 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 163 | C25 | — | 9 | 1 | no | — |
| 164 | C22×D4 | — | 27 | 1 | no | — |
| 165 | #120 | — | 9 | 1 | no | — |
| 166 | #120 | — | 27 | 1 | no | — |
| 167 | #120 | — | 27 | 1 | no | — |
| 168 | #120 | (C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 169 | C2×C22⋊C4 | — | 27 | 1 | no | — |
| 170 | H(3,𝔽3) | — | 16 | 1 | no | Sylow |
| 171 | C23×C3 | — | 3 | 3 | no | — |
| 172 | C23×C3 | — | 3 | 1 | no | — |
| 173 | C23×C3 | — | 3 | 1 | no | — |
| 174 | C23×C3 | — | 6 | 2 | no | — |
| 175 | C23×C3 | — | 6 | 6 | no | — |
| 176 | C23×C3 | D3×A4 | 1 | 1 | yes | characteristic |
| 177 | C22×D3 | — | 3 | 1 | no | — |
| 178 | C22×D3 | — | 3 | 1 | no | — |
| 179 | C22×D3 | — | 6 | 2 | no | — |
| 180 | C22×D3 | — | 9 | 1 | no | — |
| 181 | C22×D3 | — | 9 | 1 | no | — |
| 182 | C22×D3 | — | 9 | 3 | no | — |
| 183 | C22×D3 | — | 9 | 2 | no | — |
| 184 | C22×D3 | — | 9 | 6 | no | — |
| 185 | C22×D3 | — | 9 | 6 | no | — |
| 186 | C22×D3 | — | 9 | 2 | no | — |
| 187 | C22×D3 | — | 9 | 1 | no | — |
| 188 | C22×D3 | — | 18 | 2 | no | — |
| 189 | C22×D3 | — | 18 | 1 | no | — |
| 190 | C22×D3 | — | 18 | 2 | no | — |
| 191 | C22×D3 | — | 18 | 6 | no | — |
| 192 | C22×D3 | — | 18 | 6 | no | — |
| 193 | C22×D3 | — | 18 | 2 | no | — |
| 194 | C22×D3 | — | 18 | 12 | no | — |
| 195 | C22×D3 | — | 18 | 4 | no | — |
| 196 | C22×D3 | — | 18 | 3 | no | — |
| 197 | C22×D3 | — | 18 | 3 | no | — |
| 198 | C22×D3 | — | 18 | 1 | no | — |
| 199 | C22×D3 | — | 18 | 2 | no | — |
| 200 | C22×D3 | — | 18 | 6 | no | — |
| 201 | C22×D3 | — | 18 | 2 | no | — |
| 202 | C22×D3 | — | 18 | 6 | no | — |
| 203 | C22×D3 | — | 18 | 6 | no | — |
| 204 | C22×D3 | — | 18 | 6 | no | — |
| 205 | C22×D3 | — | 18 | 12 | no | — |
| 206 | C22×D3 | — | 18 | 4 | no | — |
| 207 | C22×D3 | — | 18 | 2 | no | — |
| 208 | C22×D3 | — | 18 | 2 | no | — |
| 209 | C2×A4 | — | 12 | 1 | no | — |
| 210 | C2×A4 | — | 24 | 1 | no | — |
| 211 | C2×A4 | — | 36 | 1 | no | — |
| 212 | C2×A4 | — | 36 | 1 | no | — |
| 213 | C2×A4 | — | 72 | 2 | no | — |
| 214 | C3×D4 | — | 6 | 2 | no | — |
| 215 | C3×D4 | — | 6 | 6 | no | — |
| 216 | C2×C3×C4 | — | 3 | 3 | no | — |
| 217 | C2×C3×C4 | — | 3 | 1 | no | — |
| 218 | #67 | — | 18 | 2 | no | — |
| 219 | #67 | — | 18 | 6 | no | — |
| 220 | #67 | — | 18 | 2 | no | — |
| 221 | #67 | — | 18 | 6 | no | — |
| 222 | C2×Dic3 | — | 9 | 3 | no | — |
| 223 | C2×Dic3 | — | 9 | 1 | no | — |
| 224 | D12 | — | 18 | 2 | no | — |
| 225 | D12 | — | 18 | 6 | no | — |
| 226 | C4×D3 | — | 18 | 1 | no | — |
| 227 | C4×D3 | — | 18 | 3 | no | — |
| 228 | C4×D3 | — | 18 | 3 | no | — |
| 229 | C4×D3 | — | 18 | 1 | no | — |
| 230 | C2×C32 | — | 3 | 1 | no | — |
| 231 | C2×C32 | — | 4 | 1 | no | — |
| 232 | C2×C32 | — | 6 | 2 | no | — |
| 233 | C2×C32 | — | 16 | 1 | no | — |
| 234 | C2×C32 | — | 32 | 1 | no | — |
| 235 | C3⋊D3 | — | 3 | 1 | no | — |
| 236 | C3⋊D3 | — | 4 | 1 | no | — |
| 237 | C3⋊D3 | — | 6 | 2 | no | — |
| 238 | C3⋊D3 | #120⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 239 | C3×D3 | — | 48 | 1 | no | — |
| 240 | C3×D3 | — | 48 | 1 | no | — |
| 241 | C24 | — | 9 | 1 | no | — |
| 242 | C24 | — | 27 | 1 | no | — |
| 243 | C24 | — | 27 | 1 | no | — |
| 244 | C24 | — | 54 | 2 | no | — |
| 245 | C24 | — | 54 | 2 | no | — |
| 246 | C24 | C2×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 247 | C2×D4 | — | 3 | 1 | no | — |
| 248 | C2×D4 | — | 27 | 1 | no | — |
| 249 | C2×D4 | — | 27 | 1 | no | — |
| 250 | C2×D4 | — | 27 | 1 | no | — |
| 251 | C2×D4 | — | 54 | 2 | no | — |
| 252 | C2×D4 | — | 54 | 2 | no | — |
| 253 | C22×C4 | — | 27 | 1 | no | — |
| 254 | C22⋊C4 | — | 3 | 1 | no | — |
| 255 | C22⋊C4 | — | 27 | 2 | no | — |
| 256 | C22⋊C4 | — | 27 | 1 | no | — |
| 257 | C22×C3 | — | 2 | 2 | no | — |
| 258 | C22×C3 | — | 3 | 6 | no | — |
| 259 | C22×C3 | — | 3 | 2 | no | — |
| 260 | C22×C3 | — | 3 | 1 | no | — |
| 261 | C22×C3 | — | 6 | 2 | no | — |
| 262 | C22×C3 | — | 6 | 1 | no | — |
| 263 | C22×C3 | — | 6 | 6 | no | — |
| 264 | C22×C3 | — | 6 | 2 | no | — |
| 265 | C22×C3 | — | 6 | 3 | no | — |
| 266 | C22×C3 | — | 6 | 2 | no | — |
| 267 | C22×C3 | — | 6 | 6 | no | — |
| 268 | C22×C3 | — | 144 | 1 | no | — |
| 269 | C22×C3 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 270 | C2×D3 | — | 9 | 1 | no | — |
| 271 | C2×D3 | — | 9 | 3 | no | — |
| 272 | C2×D3 | — | 9 | 3 | no | — |
| 273 | C2×D3 | — | 9 | 1 | no | — |
| 274 | C2×D3 | — | 9 | 6 | no | — |
| 275 | C2×D3 | — | 9 | 2 | no | — |
| 276 | C2×D3 | — | 12 | 1 | no | — |
| 277 | C2×D3 | — | 18 | 2 | no | — |
| 278 | C2×D3 | — | 18 | 6 | no | — |
| 279 | C2×D3 | — | 18 | 6 | no | — |
| 280 | C2×D3 | — | 18 | 12 | no | — |
| 281 | C2×D3 | — | 18 | 2 | no | — |
| 282 | C2×D3 | — | 18 | 4 | no | — |
| 283 | C2×D3 | — | 18 | 1 | no | — |
| 284 | C2×D3 | — | 18 | 6 | no | — |
| 285 | C2×D3 | — | 18 | 2 | no | — |
| 286 | C2×D3 | — | 18 | 6 | no | — |
| 287 | C2×D3 | — | 18 | 6 | no | — |
| 288 | C2×D3 | — | 18 | 12 | no | — |
| 289 | C2×D3 | — | 18 | 4 | no | — |
| 290 | C2×D3 | — | 18 | 2 | no | — |
| 291 | C2×D3 | — | 18 | 2 | no | — |
| 292 | C2×D3 | — | 18 | 3 | no | — |
| 293 | C2×D3 | — | 36 | 1 | no | — |
| 294 | C2×D3 | — | 36 | 1 | no | — |
| 295 | C2×D3 | — | 36 | 3 | no | — |
| 296 | A4 | — | 12 | 1 | no | — |
| 297 | A4 | — | 24 | 2 | no | — |
| 298 | A4 | — | 24 | 1 | no | — |
| 299 | A4 | — | 48 | 2 | no | — |
| 300 | C3×C4 | — | 6 | 3 | no | — |
| 301 | C3×C4 | — | 6 | 1 | no | — |
| 302 | Dic3 | — | 18 | 3 | no | — |
| 303 | Dic3 | — | 18 | 1 | no | — |
| 304 | C32 | — | 16 | 1 | no | — |
| 305 | C32 | — | 32 | 1 | no | — |
| 306 | C32 | C2×#120⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 307 | C23 | — | 3 | 1 | no | — |
| 308 | C23 | — | 6 | 2 | no | — |
| 309 | C23 | — | 9 | 1 | no | — |
| 310 | C23 | — | 9 | 1 | no | — |
| 311 | C23 | — | 18 | 2 | no | — |
| 312 | C23 | — | 27 | 2 | no | — |
| 313 | C23 | — | 27 | 2 | no | — |
| 314 | C23 | — | 27 | 1 | no | — |
| 315 | C23 | — | 54 | 2 | no | — |
| 316 | C23 | — | 54 | 2 | no | — |
| 317 | C23 | — | 54 | 1 | no | — |
| 318 | C23 | — | 54 | 2 | no | — |
| 319 | C23 | — | 54 | 2 | no | — |
| 320 | C23 | — | 54 | 4 | no | — |
| 321 | C23 | — | 54 | 1 | no | — |
| 322 | C23 | — | 54 | 2 | no | — |
| 323 | C23 | — | 54 | 2 | no | — |
| 324 | C23 | — | 54 | 4 | no | — |
| 325 | C23 | (C3⋊D3)⋊A4 | 1 | 1 | yes | characteristic, complemented |
| 326 | D4 | — | 6 | 2 | no | — |
| 327 | D4 | — | 54 | 2 | no | — |
| 328 | D4 | — | 54 | 2 | no | — |
| 329 | D4 | — | 54 | 2 | no | — |
| 330 | C2×C4 | — | 3 | 1 | no | — |
| 331 | C2×C4 | — | 27 | 1 | no | — |
| 332 | C2×C4 | — | 54 | 1 | no | — |
| 333 | C2×C4 | — | 54 | 1 | no | — |
| 334 | C2×C3 | — | 3 | 3 | no | — |
| 335 | C2×C3 | — | 3 | 1 | no | — |
| 336 | C2×C3 | — | 4 | 1 | no | — |
| 337 | C2×C3 | — | 6 | 6 | no | — |
| 338 | C2×C3 | — | 6 | 2 | no | — |
| 339 | C2×C3 | — | 12 | 1 | no | — |
| 340 | C2×C3 | — | 48 | 1 | no | — |
| 341 | C2×C3 | — | 96 | 1 | no | — |
| 342 | C2×C3 | — | 144 | 1 | no | — |
| 343 | C2×C3 | — | 144 | 1 | no | — |
| 344 | D3 | — | 3 | 1 | no | — |
| 345 | D3 | — | 9 | 1 | no | — |
| 346 | D3 | — | 9 | 3 | no | — |
| 347 | D3 | — | 9 | 1 | no | — |
| 348 | D3 | — | 12 | 1 | no | — |
| 349 | D3 | — | 18 | 6 | no | — |
| 350 | D3 | — | 18 | 2 | no | — |
| 351 | D3 | — | 36 | 1 | no | — |
| 352 | C22 | — | 2 | 2 | no | — |
| 353 | C22 | — | 3 | 2 | no | — |
| 354 | C22 | — | 6 | 1 | no | — |
| 355 | C22 | — | 6 | 2 | no | — |
| 356 | C22 | — | 6 | 2 | no | — |
| 357 | C22 | — | 27 | 1 | no | — |
| 358 | C22 | — | 27 | 1 | no | — |
| 359 | C22 | — | 27 | 2 | no | — |
| 360 | C22 | — | 36 | 1 | no | — |
| 361 | C22 | — | 54 | 1 | no | — |
| 362 | C22 | — | 54 | 2 | no | — |
| 363 | C22 | — | 54 | 2 | no | — |
| 364 | C22 | — | 54 | 2 | no | — |
| 365 | C22 | — | 54 | 4 | no | — |
| 366 | C22 | — | 54 | 2 | no | — |
| 367 | C22 | — | 54 | 2 | no | — |
| 368 | C22 | — | 54 | 4 | no | — |
| 369 | C22 | — | 108 | 1 | no | — |
| 370 | C22 | C2×(C3⋊D3)⋊A4 | 1 | 1 | yes | characteristic |
| 371 | C4 | — | 6 | 1 | no | — |
| 372 | C4 | — | 54 | 1 | no | — |
| 373 | C3 | — | 3 | 1 | no | — |
| 374 | C3 | — | 48 | 1 | no | — |
| 375 | C3 | — | 96 | 1 | no | — |
| 376 | C3 | D3×#120⋊C3 | 1 | 1 | yes | characteristic |
| 377 | C2 | — | 3 | 1 | no | — |
| 378 | C2 | — | 4 | 1 | no | — |
| 379 | C2 | — | 6 | 2 | no | — |
| 380 | C2 | — | 9 | 1 | no | — |
| 381 | C2 | — | 27 | 1 | no | — |
| 382 | C2 | — | 36 | 1 | no | — |
| 383 | C2 | — | 54 | 2 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C24×C32 | C22×C3 |
| Frattini, socle | C22×C3 | C2×D3×A4 |
| Fitting | C32×#120 | C2×C3 |
| LCS | G ▷ C24×C32 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. (C3⋊D3)⋊(C22⋊A4) | C2 | semidirect |
| 2. #120⋊H(3,𝔽3) | C2 | semidirect |
| 3. #11720769 | C2 | semidirect |
| 4. C3⋊D3×#120 | C3 | semidirect |
| 6. C32⋊(C22⋊A4) | C22 | semidirect |
| 8. C24×C3⋊D3 | C2×C3 | semidirect |
| 11. C32×#120 | C2×C3 | semidirect |
| 12. #64162 | C2×C3 | semidirect |
| 17. C3×#120⋊C3 | D3 | semidirect |
| 26. C24×C32 | C22×C3 | semidirect |
| 31. C23×C3⋊D3 | A4 | semidirect |
| 33. C3×C22⋊A4 | C2×D3 | semidirect |
| 68. C23×C32 | C2×A4 | semidirect |
| 84. C22×C3⋊D3 | C2×A4 | semidirect |
| 168. #120 | (C3⋊D3)⋊C3 | semidirect |
| 238. C3⋊D3 | #120⋊C3 | semidirect |
| 246. C24 | C2×(C3⋊D3)⋊C3 | semidirect |
| 306. C32 | C2×#120⋊C3 | semidirect |
| 325. C23 | (C3⋊D3)⋊A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C3⋊D3)⋊(C22⋊A4) | 2 |
| #120⋊H(3,𝔽3) | 2 |
| #11720769 | 2 |
| C3⋊D3×#120 | 3 |
| D3×#120⋊C3 | 3 |
| C2×(C3⋊D3)⋊A4 | 4 |