Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
991 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 991 conjugacy classes of subgroups — too many to draw. Only its 135 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 | #11722520 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | Q16×#272 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #64128⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11721239 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11721228 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11720855 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11720838 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C8×((C3⋊D3)⋊C3)⋊C2 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | D3×#919 | — | 3 | 2 | no | maximal |
| 10 | Q8×#272 | C22 | 1 | 2 | yes | — |
| 11 | #88722 | C22 | 1 | 4 | yes | complemented |
| 12 | #88655 | — | 2 | 2 | no | — |
| 13 | #88655 | C22 | 1 | 2 | yes | — |
| 14 | C4×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 2 | no | — |
| 15 | C4×((C3⋊D3)⋊C3)⋊C2 | C22 | 1 | 1 | yes | characteristic |
| 16 | #88648 | — | 2 | 4 | no | — |
| 17 | #88648 | C22 | 1 | 4 | yes | complemented |
| 18 | Q16×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #88550 | C22 | 1 | 2 | yes | complemented |
| 20 | #88530 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C8×#272 | C22 | 1 | 1 | yes | characteristic |
| 22 | #3755⋊C3 | C22 | 1 | 4 | yes | complemented |
| 23 | #3745⋊C3 | C22 | 1 | 2 | yes | complemented |
| 24 | C8×(C3⋊D3)⋊C3 | C22 | 1 | 2 | yes | complemented |
| 25 | #88438 | C22 | 1 | 4 | yes | complemented |
| 26 | #88434 | C22 | 1 | 1 | yes | characteristic |
| 27 | #88432 | C22 | 1 | 2 | yes | complemented |
| 28 | ((C3⋊D3)⋊C3)⋊C8 | C22 | 1 | 2 | yes | complemented |
| 29 | D3×#239 | — | 3 | 4 | no | — |
| 30 | #64128 | D3 | 1 | 2 | yes | complemented |
| 31 | C3×#919 | — | 3 | 2 | no | — |
| 32 | C3×D3×Q16 | — | 3 | 2 | no | — |
| 33 | C3×D3×Q16 | — | 6 | 1 | no | — |
| 34 | #63950 | — | 3 | 4 | no | — |
| 35 | #63949 | — | 3 | 4 | no | — |
| 36 | D3×#215 | — | 3 | 4 | no | — |
| 37 | #63810 | — | 3 | 2 | no | — |
| 38 | #63808 | — | 3 | 2 | no | — |
| 39 | D3×D24 | — | 3 | 2 | no | — |
| 40 | D32×C8 | — | 3 | 2 | no | — |
| 41 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 2 | no | — |
| 42 | C2×((C3⋊D3)⋊C3)⋊C2 | D4 | 1 | 1 | yes | characteristic |
| 43 | Q8×H(3,𝔽3) | C23 | 1 | 2 | yes | — |
| 44 | C4×#272 | — | 2 | 2 | no | — |
| 45 | C4×#272 | C23 | 1 | 1 | yes | characteristic |
| 46 | #6229 | — | 2 | 2 | no | — |
| 47 | #6229 | C23 | 1 | 2 | yes | — |
| 48 | C4⋊((C3⋊D3)⋊C3) | — | 2 | 4 | no | — |
| 49 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 4 | yes | — |
| 50 | C4×(C3⋊D3)⋊C3 | — | 2 | 4 | no | — |
| 51 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 2 | yes | — |
| 52 | #6199 | D4 | 1 | 1 | yes | characteristic |
| 53 | #6198 | — | 2 | 4 | no | — |
| 54 | #6198 | — | 2 | 2 | no | — |
| 55 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 4 | no | — |
| 56 | ((C3⋊D3)⋊C3)⋊C4 | D4 | 1 | 2 | yes | — |
| 57 | C8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 58 | #6180 | C23 | 1 | 1 | yes | characteristic |
| 59 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 2 | yes | — |
| 60 | D3×#135 | — | 9 | 2 | no | — |
| 61 | C2×#919 | — | 9 | 1 | no | — |
| 62 | #3832 | C2×D3 | 1 | 4 | yes | complemented |
| 63 | C3×#239 | — | 3 | 4 | no | — |
| 64 | C3×D3×Q8 | — | 3 | 4 | no | — |
| 65 | C3×D3×Q8 | — | 6 | 2 | no | — |
| 66 | D3×D12 | — | 3 | 4 | no | — |
| 67 | D3×D12 | — | 6 | 4 | no | — |
| 68 | C4×D32 | — | 3 | 2 | no | — |
| 69 | C4×D32 | — | 6 | 4 | no | — |
| 70 | #3799 | — | 3 | 4 | no | — |
| 71 | #3799 | — | 6 | 4 | no | — |
| 72 | #3796 | — | 3 | 4 | no | — |
| 73 | #3796 | — | 6 | 4 | no | — |
| 74 | C32×Q16 | — | 2 | 1 | no | — |
| 75 | C32×Q16 | C2×D3 | 1 | 2 | yes | complemented |
| 76 | #3755 | C2×D3 | 1 | 4 | yes | complemented |
| 77 | #3745 | C2×D3 | 1 | 2 | yes | complemented |
| 78 | C8×C3⋊D3 | C2×D3 | 1 | 2 | yes | complemented |
| 79 | C3×#216 | — | 3 | 4 | no | — |
| 80 | C3×#216 | — | 6 | 2 | no | — |
| 81 | C3×#215 | — | 3 | 4 | no | — |
| 82 | C3×Dic12 | — | 3 | 2 | no | — |
| 83 | C3×Dic12 | — | 6 | 1 | no | — |
| 84 | C3×D24 | — | 3 | 2 | no | — |
| 85 | C3×D3×C8 | — | 3 | 2 | no | — |
| 86 | C3×D3×C8 | — | 3 | 2 | no | — |
| 87 | C3×D3×C8 | — | 6 | 1 | no | — |
| 88 | #3717 | — | 3 | 4 | no | — |
| 89 | #3715 | — | 3 | 4 | no | — |
| 90 | #3714 | — | 3 | 4 | no | — |
| 91 | #3710 | — | 3 | 2 | no | — |
| 92 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 93 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 94 | C2×#272 | C2×D4 | 1 | 1 | yes | characteristic |
| 95 | C2×(C3⋊D3)⋊C3 | — | 2 | 4 | no | — |
| 96 | C2×(C3⋊D3)⋊C3 | C2×D4 | 1 | 2 | yes | — |
| 97 | ((C3⋊D3)⋊C3)⋊C2 | — | 2 | 2 | no | — |
| 98 | ((C3⋊D3)⋊C3)⋊C2 | — | 4 | 4 | no | — |
| 99 | C4×H(3,𝔽3) | — | 2 | 2 | no | — |
| 100 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 101 | #1084 | — | 2 | 2 | no | — |
| 102 | #1084 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | (C3⋊Dic3)⋊C3 | C2×D4 | 1 | 2 | yes | — |
| 104 | D3×#41 | — | 9 | 4 | no | — |
| 105 | C2×#239 | — | 9 | 2 | no | — |
| 106 | C3×#135 | — | 9 | 2 | no | — |
| 107 | C2×C3×Q16 | — | 9 | 1 | no | — |
| 108 | #950 | — | 9 | 4 | no | — |
| 109 | C2×#215 | — | 9 | 2 | no | — |
| 110 | #919 | — | 3 | 2 | no | — |
| 111 | #919 | — | 9 | 2 | no | — |
| 112 | #919 | — | 9 | 2 | no | — |
| 113 | #919 | — | 9 | 4 | no | — |
| 114 | D3×Q16 | — | 3 | 2 | no | — |
| 115 | D3×Q16 | — | 6 | 1 | no | — |
| 116 | #916 | — | 9 | 4 | no | — |
| 117 | D3×SD16 | — | 9 | 4 | no | — |
| 118 | #912 | — | 9 | 2 | no | — |
| 119 | D3×D8 | — | 9 | 2 | no | — |
| 120 | #904 | — | 9 | 2 | no | — |
| 121 | C2×D24 | — | 9 | 1 | no | — |
| 122 | C2×D3×C8 | — | 9 | 1 | no | — |
| 123 | C2×D3×C8 | — | 9 | 2 | no | — |
| 124 | C2×D32 | — | 3 | 2 | no | — |
| 125 | C2×D32 | — | 6 | 4 | no | — |
| 126 | C32×Q8 | — | 2 | 2 | no | — |
| 127 | C32×Q8 | C22×D3 | 1 | 4 | yes | — |
| 128 | C4⋊(C3⋊D3) | — | 2 | 4 | no | — |
| 129 | C4⋊(C3⋊D3) | C22×D3 | 1 | 4 | yes | — |
| 130 | C4×C3⋊D3 | — | 2 | 4 | no | — |
| 131 | C4×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 132 | C3×D12 | — | 3 | 4 | no | — |
| 133 | C3×D12 | — | 6 | 4 | no | — |
| 134 | C3×C4×D3 | — | 3 | 2 | no | — |
| 135 | C3×C4×D3 | — | 3 | 2 | no | — |
| 136 | C3×C4×D3 | — | 6 | 1 | no | — |
| 137 | C3×C4×D3 | — | 6 | 4 | no | — |
| 138 | C3×C4×D3 | — | 6 | 4 | no | — |
| 139 | C3×C4×D3 | — | 12 | 2 | no | — |
| 140 | C3×Dic6 | — | 3 | 4 | no | — |
| 141 | C3×Dic6 | — | 6 | 2 | no | — |
| 142 | C3×Dic6 | — | 6 | 4 | no | — |
| 143 | C3×Dic6 | — | 12 | 2 | no | — |
| 144 | #626 | — | 6 | 4 | no | — |
| 145 | #626 | — | 6 | 4 | no | — |
| 146 | #626 | — | 6 | 4 | no | — |
| 147 | #624 | — | 3 | 2 | no | — |
| 148 | #624 | — | 6 | 4 | no | — |
| 149 | D3×Dic3 | — | 3 | 2 | no | — |
| 150 | D3×Dic3 | — | 3 | 2 | no | — |
| 151 | D3×Dic3 | — | 6 | 4 | no | — |
| 152 | C32×C8 | — | 2 | 1 | no | — |
| 153 | C32×C8 | C22×D3 | 1 | 2 | yes | — |
| 154 | C3⋊(C3⋊C8) | C22×D3 | 1 | 2 | yes | — |
| 155 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 156 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 157 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 158 | C2×#135 | — | 27 | 1 | no | Sylow |
| 159 | C2×H(3,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 160 | #272 | #135 | 1 | 2 | yes | complemented |
| 161 | (C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 162 | (C3⋊D3)⋊C3 | — | 4 | 4 | no | — |
| 163 | C3×#41 | — | 9 | 4 | no | — |
| 164 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 165 | #239 | — | 3 | 4 | no | — |
| 166 | #239 | — | 9 | 4 | no | — |
| 167 | #239 | — | 9 | 4 | no | — |
| 168 | #239 | — | 18 | 4 | no | — |
| 169 | D3×Q8 | — | 3 | 4 | no | — |
| 170 | D3×Q8 | — | 6 | 2 | no | — |
| 171 | #237 | — | 9 | 4 | no | — |
| 172 | #237 | — | 18 | 4 | no | — |
| 173 | D3×D4 | — | 9 | 4 | no | — |
| 174 | D3×D4 | — | 18 | 4 | no | — |
| 175 | #235 | — | 9 | 4 | no | — |
| 176 | #235 | — | 18 | 4 | no | — |
| 177 | C2×D12 | — | 9 | 2 | no | — |
| 178 | C2×D12 | — | 18 | 2 | no | — |
| 179 | C2×C4×D3 | — | 9 | 1 | no | — |
| 180 | C2×C4×D3 | — | 9 | 2 | no | — |
| 181 | C2×C4×D3 | — | 18 | 2 | no | — |
| 182 | C2×C4×D3 | — | 18 | 4 | no | — |
| 183 | C3×Q16 | — | 3 | 2 | no | — |
| 184 | C3×Q16 | — | 6 | 1 | no | — |
| 185 | C3×Q16 | — | 9 | 2 | no | — |
| 186 | C3×Q16 | — | 9 | 1 | no | — |
| 187 | C3×Q16 | D32 | 1 | 1 | yes | characteristic |
| 188 | C3×SD16 | — | 9 | 4 | no | — |
| 189 | C3×D8 | — | 9 | 2 | no | — |
| 190 | C2×C3×C8 | — | 9 | 2 | no | — |
| 191 | C2×C3×C8 | — | 9 | 1 | no | — |
| 192 | #216 | — | 3 | 4 | no | — |
| 193 | #216 | — | 6 | 2 | no | — |
| 194 | #215 | — | 3 | 4 | no | — |
| 195 | #215 | — | 9 | 4 | no | — |
| 196 | #215 | — | 9 | 4 | no | — |
| 197 | #214 | — | 9 | 4 | no | — |
| 198 | #213 | — | 9 | 4 | no | — |
| 199 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 200 | C2×C3⋊C8 | — | 9 | 2 | no | — |
| 201 | Dic12 | — | 3 | 2 | no | — |
| 202 | Dic12 | — | 6 | 1 | no | — |
| 203 | D24 | — | 3 | 2 | no | — |
| 204 | D24 | — | 9 | 2 | no | — |
| 205 | D24 | — | 9 | 2 | no | — |
| 206 | #204 | — | 9 | 4 | no | — |
| 207 | D3×C8 | — | 3 | 2 | no | — |
| 208 | D3×C8 | — | 3 | 2 | no | — |
| 209 | D3×C8 | — | 6 | 1 | no | — |
| 210 | D3×C8 | — | 9 | 2 | no | — |
| 211 | D3×C8 | — | 9 | 2 | no | — |
| 212 | D3×C8 | — | 9 | 2 | no | — |
| 213 | D3×C8 | — | 9 | 2 | no | — |
| 214 | C2×C3⋊D3 | — | 2 | 4 | no | — |
| 215 | C2×C3⋊D3 | D3×D4 | 1 | 2 | yes | — |
| 216 | C2×C3×D3 | — | 3 | 2 | no | — |
| 217 | C2×C3×D3 | — | 3 | 2 | no | — |
| 218 | C2×C3×D3 | — | 6 | 1 | no | — |
| 219 | C2×C3×D3 | — | 6 | 4 | no | — |
| 220 | D32 | — | 6 | 4 | no | — |
| 221 | D32 | — | 12 | 8 | no | — |
| 222 | C32×C4 | — | 2 | 4 | no | — |
| 223 | C32×C4 | — | 2 | 1 | no | — |
| 224 | C32×C4 | — | 4 | 2 | no | — |
| 225 | C32×C4 | C23×D3 | 1 | 2 | yes | — |
| 226 | C3⋊Dic3 | D3×D4 | 1 | 2 | yes | — |
| 227 | C3×Dic3 | — | 3 | 2 | no | — |
| 228 | C3×Dic3 | — | 3 | 2 | no | — |
| 229 | C3×Dic3 | — | 6 | 1 | no | — |
| 230 | C3×Dic3 | — | 6 | 4 | no | — |
| 231 | C3×Dic3 | — | 12 | 2 | no | — |
| 232 | C2×#41 | — | 27 | 2 | no | — |
| 233 | #135 | — | 9 | 2 | no | — |
| 234 | #135 | — | 27 | 2 | no | — |
| 235 | #135 | — | 27 | 4 | no | — |
| 236 | C2×Q16 | — | 9 | 1 | no | — |
| 237 | C2×SD16 | — | 27 | 2 | no | — |
| 238 | C2×D8 | — | 27 | 1 | no | — |
| 239 | C22×C8 | — | 27 | 1 | no | — |
| 240 | H(3,𝔽3) | C2×#135 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 241 | C22×D3 | — | 9 | 1 | no | — |
| 242 | C22×D3 | — | 9 | 2 | no | — |
| 243 | C22×D3 | — | 18 | 4 | no | — |
| 244 | C22×D3 | — | 18 | 2 | no | — |
| 245 | C3×Q8 | — | 3 | 4 | no | — |
| 246 | C3×Q8 | — | 6 | 2 | no | — |
| 247 | C3×Q8 | — | 9 | 2 | no | — |
| 248 | C3×Q8 | — | 18 | 2 | no | — |
| 249 | C3×Q8 | C2×D32 | 1 | 2 | yes | — |
| 250 | C3×D4 | — | 9 | 4 | no | — |
| 251 | C3×D4 | — | 18 | 4 | no | — |
| 252 | C2×C3×C4 | — | 9 | 2 | no | — |
| 253 | C2×C3×C4 | — | 9 | 1 | no | — |
| 254 | C2×C3×C4 | — | 18 | 2 | no | — |
| 255 | C2×C3×C4 | — | 18 | 4 | no | — |
| 256 | #67 | — | 18 | 4 | no | — |
| 257 | #67 | — | 18 | 4 | no | — |
| 258 | #67 | — | 18 | 4 | no | — |
| 259 | C2×Dic3 | — | 9 | 1 | no | — |
| 260 | C2×Dic3 | — | 9 | 2 | no | — |
| 261 | C2×Dic3 | — | 18 | 4 | no | — |
| 262 | D12 | — | 3 | 4 | no | — |
| 263 | D12 | — | 6 | 4 | no | — |
| 264 | D12 | — | 9 | 4 | no | — |
| 265 | D12 | — | 18 | 4 | no | — |
| 266 | D12 | — | 18 | 2 | no | — |
| 267 | D12 | — | 18 | 4 | no | — |
| 268 | C4×D3 | — | 3 | 2 | no | — |
| 269 | C4×D3 | — | 3 | 2 | no | — |
| 270 | C4×D3 | — | 6 | 1 | no | — |
| 271 | C4×D3 | — | 6 | 4 | no | — |
| 272 | C4×D3 | — | 6 | 4 | no | — |
| 273 | C4×D3 | — | 9 | 2 | no | — |
| 274 | C4×D3 | — | 9 | 2 | no | — |
| 275 | C4×D3 | — | 9 | 2 | no | — |
| 276 | C4×D3 | — | 9 | 2 | no | — |
| 277 | C4×D3 | — | 12 | 2 | no | — |
| 278 | C4×D3 | — | 18 | 4 | no | — |
| 279 | C4×D3 | — | 18 | 4 | no | — |
| 280 | C4×D3 | — | 18 | 4 | no | — |
| 281 | Dic6 | — | 3 | 4 | no | — |
| 282 | Dic6 | — | 6 | 2 | no | — |
| 283 | Dic6 | — | 6 | 4 | no | — |
| 284 | Dic6 | — | 12 | 2 | no | — |
| 285 | C3×C8 | — | 3 | 2 | no | — |
| 286 | C3×C8 | — | 6 | 1 | no | — |
| 287 | C3×C8 | — | 9 | 2 | no | — |
| 288 | C3×C8 | — | 9 | 1 | no | — |
| 289 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 290 | C3⋊C8 | — | 3 | 2 | no | — |
| 291 | C3⋊C8 | — | 3 | 2 | no | — |
| 292 | C3⋊C8 | — | 6 | 1 | no | — |
| 293 | C3⋊C8 | — | 9 | 2 | no | — |
| 294 | C2×C32 | — | 2 | 1 | no | — |
| 295 | C2×C32 | C2×D3×D4 | 1 | 2 | yes | — |
| 296 | C3⋊D3 | — | 2 | 2 | no | — |
| 297 | C3⋊D3 | — | 4 | 4 | no | — |
| 298 | C3×D3 | — | 3 | 4 | no | — |
| 299 | C3×D3 | — | 6 | 2 | no | — |
| 300 | C3×D3 | — | 6 | 2 | no | — |
| 301 | C3×D3 | — | 12 | 4 | no | — |
| 302 | #41 | — | 9 | 4 | no | — |
| 303 | #41 | — | 27 | 4 | no | — |
| 304 | #41 | — | 54 | 4 | no | — |
| 305 | C2×Q8 | — | 9 | 2 | no | — |
| 306 | C2×D4 | — | 27 | 2 | no | — |
| 307 | C2×D4 | — | 54 | 2 | no | — |
| 308 | C22×C4 | — | 27 | 1 | no | — |
| 309 | C22×C4 | — | 54 | 2 | no | — |
| 310 | Q16 | — | 9 | 2 | no | — |
| 311 | Q16 | — | 9 | 1 | no | — |
| 312 | Q16 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 313 | SD16 | — | 9 | 4 | no | — |
| 314 | SD16 | — | 27 | 4 | no | — |
| 315 | D8 | — | 9 | 2 | no | — |
| 316 | D8 | — | 27 | 2 | no | — |
| 317 | C2×C8 | — | 9 | 1 | no | — |
| 318 | C2×C8 | — | 9 | 2 | no | — |
| 319 | C2×C8 | — | 27 | 1 | no | — |
| 320 | C2×C8 | — | 27 | 2 | no | — |
| 321 | C22×C3 | — | 9 | 2 | no | — |
| 322 | C22×C3 | — | 9 | 1 | no | — |
| 323 | C22×C3 | — | 18 | 4 | no | — |
| 324 | C2×D3 | — | 3 | 2 | no | — |
| 325 | C2×D3 | — | 3 | 2 | no | — |
| 326 | C2×D3 | — | 6 | 1 | no | — |
| 327 | C2×D3 | — | 6 | 4 | no | — |
| 328 | C2×D3 | — | 9 | 2 | no | — |
| 329 | C2×D3 | — | 18 | 4 | no | — |
| 330 | C2×D3 | — | 18 | 4 | no | — |
| 331 | C2×D3 | — | 18 | 2 | no | — |
| 332 | C2×D3 | — | 36 | 8 | no | — |
| 333 | C2×D3 | — | 36 | 4 | no | — |
| 334 | C3×C4 | — | 2 | 2 | no | — |
| 335 | C3×C4 | — | 3 | 2 | no | — |
| 336 | C3×C4 | — | 6 | 4 | no | — |
| 337 | C3×C4 | — | 6 | 1 | no | — |
| 338 | C3×C4 | — | 9 | 2 | no | — |
| 339 | C3×C4 | — | 9 | 1 | no | — |
| 340 | C3×C4 | — | 12 | 2 | no | — |
| 341 | C3×C4 | — | 18 | 2 | no | — |
| 342 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 343 | Dic3 | — | 3 | 2 | no | — |
| 344 | Dic3 | — | 3 | 2 | no | — |
| 345 | Dic3 | — | 6 | 1 | no | — |
| 346 | Dic3 | — | 6 | 4 | no | — |
| 347 | Dic3 | — | 9 | 2 | no | — |
| 348 | Dic3 | — | 12 | 2 | no | — |
| 349 | C32 | — | 2 | 1 | no | — |
| 350 | C32 | D3×#135 | 1 | 2 | yes | complemented |
| 351 | C23 | — | 27 | 1 | no | — |
| 352 | C23 | — | 54 | 2 | no | — |
| 353 | Q8 | — | 9 | 2 | no | — |
| 354 | Q8 | — | 18 | 2 | no | — |
| 355 | Q8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 2 | yes | — |
| 356 | D4 | — | 9 | 4 | no | — |
| 357 | D4 | — | 18 | 4 | no | — |
| 358 | D4 | — | 54 | 2 | no | — |
| 359 | D4 | — | 54 | 4 | no | — |
| 360 | C2×C4 | — | 9 | 1 | no | — |
| 361 | C2×C4 | — | 9 | 2 | no | — |
| 362 | C2×C4 | — | 18 | 4 | no | — |
| 363 | C2×C4 | — | 18 | 2 | no | — |
| 364 | C2×C4 | — | 27 | 1 | no | — |
| 365 | C2×C4 | — | 27 | 2 | no | — |
| 366 | C2×C4 | — | 54 | 4 | no | — |
| 367 | C8 | — | 9 | 1 | no | — |
| 368 | C8 | — | 9 | 2 | no | — |
| 369 | C8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 370 | C2×C3 | — | 3 | 2 | no | — |
| 371 | C2×C3 | — | 6 | 1 | no | — |
| 372 | C2×C3 | — | 9 | 2 | no | — |
| 373 | C2×C3 | — | 18 | 2 | no | — |
| 374 | C2×C3 | — | 36 | 4 | no | — |
| 375 | C2×C3 | D32×D4 | 1 | 1 | yes | characteristic |
| 376 | D3 | — | 3 | 4 | no | — |
| 377 | D3 | — | 6 | 2 | no | — |
| 378 | D3 | — | 6 | 2 | no | — |
| 379 | D3 | — | 12 | 4 | no | — |
| 380 | D3 | — | 18 | 2 | no | — |
| 381 | D3 | — | 36 | 4 | no | — |
| 382 | C22 | — | 9 | 1 | no | — |
| 383 | C22 | — | 9 | 2 | no | — |
| 384 | C22 | — | 18 | 4 | no | — |
| 385 | C22 | — | 54 | 2 | no | — |
| 386 | C22 | — | 108 | 4 | no | — |
| 387 | C4 | — | 2 | 2 | no | — |
| 388 | C4 | — | 9 | 2 | no | — |
| 389 | C4 | — | 9 | 1 | no | — |
| 390 | C4 | — | 18 | 2 | no | — |
| 391 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 392 | C3 | — | 3 | 2 | no | — |
| 393 | C3 | — | 6 | 1 | no | — |
| 394 | C3 | #10594764 | 1 | 1 | yes | characteristic |
| 395 | C2 | — | 9 | 2 | no | — |
| 396 | C2 | — | 18 | 2 | no | — |
| 397 | C2 | — | 36 | 4 | no | — |
| 398 | C2 | D4×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722520 | C2 | semidirect |
| 2. Q16×#272 | C2 | semidirect |
| 3. #64128⋊C3 | C2 | semidirect |
| 4. #11721239 | C2 | semidirect |
| 5. #11721228 | C2 | semidirect |
| 6. #11720855 | C2 | semidirect |
| 7. #11720838 | C2 | semidirect |
| 8. C8×((C3⋊D3)⋊C3)⋊C2 | C2 | semidirect |
| 11. #88722 | C22 | semidirect |
| 17. #88648 | C22 | semidirect |
| 18. Q16×H(3,𝔽3) | C22 | semidirect |
| 19. #88550 | C22 | semidirect |
| 20. #88530 | C22 | semidirect |
| 22. #3755⋊C3 | C22 | semidirect |
| 23. #3745⋊C3 | C22 | semidirect |
| 24. C8×(C3⋊D3)⋊C3 | C22 | semidirect |
| 25. #88438 | C22 | semidirect |
| 27. #88432 | C22 | semidirect |
| 28. ((C3⋊D3)⋊C3)⋊C8 | C22 | semidirect |
| 30. #64128 | D3 | semidirect |
| 62. #3832 | C2×D3 | semidirect |
| 75. C32×Q16 | C2×D3 | semidirect |
| 76. #3755 | C2×D3 | semidirect |
| 77. #3745 | C2×D3 | semidirect |
| 78. C8×C3⋊D3 | C2×D3 | semidirect |
| 160. #272 | #135 | semidirect |
| 240. H(3,𝔽3) | C2×#135 | semidirect |
| 312. Q16 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 350. C32 | D3×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722520 | 2 |
| Q16×#272 | 2 |
| #64128⋊C3 | 2 |
| #11721239 | 2 |
| #11721228 | 2 |
| #11720855 | 2 |
| #11720838 | 2 |
| C8×((C3⋊D3)⋊C3)⋊C2 | 2 |
| D3×#919 | 3 |