Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
228 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 36 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 | #13129779 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13129714 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13116061 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11719215 | C4 | 1 | 1 | yes | characteristic |
| 5 | C2×#88112 | — | 2 | 1 | no | — |
| 6 | C2×#88065 | — | 2 | 1 | no | — |
| 7 | #11718794 | — | 2 | 1 | no | — |
| 8 | #11718637 | C22 | 1 | 1 | yes | characteristic |
| 9 | #11718285 | — | 2 | 1 | no | — |
| 10 | C13×#343 | C4 | 1 | 1 | yes | characteristic |
| 11 | C2×#6127 | — | 2 | 1 | no | — |
| 12 | C22×#1057 | — | 4 | 1 | no | — |
| 13 | C2×C13×M16 | — | 2 | 1 | no | — |
| 14 | C2×C13×C4⋊C4 | C2×C4 | 1 | 1 | yes | characteristic |
| 15 | #88184 | — | 4 | 1 | no | — |
| 16 | C2×C4⋊Dic13 | D4 | 1 | 1 | yes | characteristic |
| 17 | C2×#6101 | — | 4 | 1 | no | — |
| 18 | C2×C4×Dic13 | D4 | 1 | 1 | yes | characteristic |
| 19 | #88151 | — | 4 | 1 | no | — |
| 20 | #88149 | — | 4 | 1 | no | — |
| 21 | C22⋊#1057 | — | 4 | 1 | no | — |
| 22 | #88112 | — | 2 | 2 | no | — |
| 23 | #88112 | — | 4 | 1 | no | — |
| 24 | #88065 | — | 4 | 1 | no | — |
| 25 | #88065 | — | 4 | 1 | no | — |
| 26 | #88061 | — | 4 | 1 | no | — |
| 27 | #88056 | — | 4 | 1 | no | — |
| 28 | #7417 | — | 13 | 1 | no | maximal, Sylow |
| 29 | C22×C4×C13 | — | 2 | 1 | no | — |
| 30 | C22×C4×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 31 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 32 | C22×Dic13 | — | 2 | 1 | no | — |
| 33 | C22×Dic13 | — | 2 | 1 | no | — |
| 34 | #6127 | — | 4 | 1 | no | — |
| 35 | #6127 | — | 4 | 1 | no | — |
| 36 | #6127 | — | 4 | 1 | no | — |
| 37 | #6127 | — | 4 | 1 | no | — |
| 38 | C2×D52 | — | 2 | 1 | no | — |
| 39 | C2×D52 | — | 4 | 1 | no | — |
| 40 | C2×C4×D13 | — | 4 | 1 | no | — |
| 41 | C2×Dic26 | — | 2 | 1 | no | — |
| 42 | C2×#1057 | — | 4 | 2 | no | — |
| 43 | C2×#1057 | — | 8 | 1 | no | — |
| 44 | C2×#1057 | — | 8 | 1 | no | — |
| 45 | C2×#1057 | — | 8 | 1 | no | — |
| 46 | C13×M16 | — | 4 | 1 | no | — |
| 47 | C13×M16 | — | 4 | 1 | no | — |
| 48 | C2×C8×C13 | — | 4 | 1 | no | — |
| 49 | C13×C4⋊C4 | — | 4 | 1 | no | — |
| 50 | #6103 | — | 4 | 2 | no | — |
| 51 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 52 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 53 | #6101 | — | 8 | 1 | no | — |
| 54 | #6101 | — | 8 | 1 | no | — |
| 55 | C4×Dic13 | — | 2 | 1 | no | — |
| 56 | C4×Dic13 | D8 | 1 | 1 | yes | characteristic |
| 57 | C4×Dic13 | SD16 | 1 | 1 | yes | characteristic |
| 58 | #2039 | — | 13 | 1 | no | — |
| 59 | #1325 | — | 13 | 1 | no | — |
| 60 | #1296 | — | 13 | 1 | no | — |
| 61 | C23×C13 | #99 | 1 | 1 | yes | characteristic |
| 62 | C22×D13 | — | 4 | 1 | no | — |
| 63 | C2×C4×C13 | — | 2 | 1 | no | — |
| 64 | C2×C4×C13 | — | 2 | 1 | no | — |
| 65 | C2×C4×C13 | — | 4 | 1 | no | — |
| 66 | C2×C4×C13 | — | 8 | 1 | no | — |
| 67 | C2×C4×C13 | #102 | 1 | 1 | yes | characteristic |
| 68 | C2×C4×C13 | #104 | 1 | 1 | yes | characteristic |
| 69 | C22⋊D13 | — | 8 | 1 | no | — |
| 70 | C22⋊D13 | — | 8 | 1 | no | — |
| 71 | C2×Dic13 | — | 2 | 1 | no | — |
| 72 | C2×Dic13 | — | 2 | 1 | no | — |
| 73 | C2×Dic13 | — | 2 | 1 | no | — |
| 74 | C2×Dic13 | — | 2 | 1 | no | — |
| 75 | C2×Dic13 | — | 2 | 1 | no | — |
| 76 | C2×Dic13 | — | 2 | 1 | no | — |
| 77 | C2×Dic13 | — | 4 | 1 | no | — |
| 78 | C2×Dic13 | — | 4 | 1 | no | — |
| 79 | C2×Dic13 | — | 8 | 1 | no | — |
| 80 | D52 | — | 4 | 1 | no | — |
| 81 | D52 | — | 4 | 1 | no | — |
| 82 | D52 | — | 16 | 1 | no | — |
| 83 | C4×D13 | — | 8 | 1 | no | — |
| 84 | C4×D13 | — | 8 | 1 | no | — |
| 85 | Dic26 | — | 4 | 1 | no | — |
| 86 | Dic26 | — | 4 | 1 | no | — |
| 87 | #1057 | — | 8 | 2 | no | — |
| 88 | #1057 | — | 16 | 1 | no | — |
| 89 | C8×C13 | — | 8 | 1 | no | — |
| 90 | #537 | — | 13 | 1 | no | — |
| 91 | C2×C4⋊C8 | — | 26 | 1 | no | — |
| 92 | C2×#104 | — | 26 | 1 | no | — |
| 93 | #417 | — | 26 | 1 | no | — |
| 94 | #384 | — | 13 | 1 | no | — |
| 95 | #343 | #261 | 1 | 1 | yes | characteristic |
| 96 | #324 | — | 26 | 1 | no | — |
| 97 | C22×C13 | — | 2 | 1 | no | — |
| 98 | C22×C13 | — | 2 | 1 | no | — |
| 99 | C22×C13 | #327 | 1 | 1 | yes | characteristic |
| 100 | C22×C13 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 101 | C22×C13 | #355 | 1 | 1 | yes | characteristic |
| 102 | C2×D13 | — | 8 | 1 | no | — |
| 103 | C2×D13 | — | 8 | 1 | no | — |
| 104 | C2×D13 | — | 8 | 1 | no | — |
| 105 | C4×C13 | — | 2 | 1 | no | — |
| 106 | C4×C13 | — | 2 | 1 | no | — |
| 107 | C4×C13 | — | 8 | 1 | no | — |
| 108 | Dic13 | — | 2 | 1 | no | — |
| 109 | Dic13 | — | 2 | 1 | no | — |
| 110 | Dic13 | — | 2 | 1 | no | — |
| 111 | Dic13 | — | 2 | 1 | no | — |
| 112 | Dic13 | — | 8 | 1 | no | — |
| 113 | Dic13 | — | 8 | 1 | no | — |
| 114 | C2×#41 | — | 26 | 1 | no | — |
| 115 | C2×M16 | — | 2 | 1 | no | — |
| 116 | C22×C8 | — | 52 | 1 | no | — |
| 117 | C22⋊Q8 | — | 52 | 1 | no | — |
| 118 | #121 | — | 52 | 1 | no | — |
| 119 | #121 | — | 52 | 1 | no | — |
| 120 | C2×C4⋊C4 | — | 13 | 1 | no | — |
| 121 | C2×C4⋊C4 | — | 52 | 1 | no | — |
| 122 | C2×C4⋊C4 | C2×#261 | 1 | 1 | yes | characteristic |
| 123 | C2×C42 | — | 13 | 1 | no | — |
| 124 | C4⋊C8 | — | 26 | 2 | no | — |
| 125 | C4⋊C8 | — | 52 | 1 | no | — |
| 126 | #104 | — | 52 | 1 | no | — |
| 127 | #104 | — | 52 | 1 | no | — |
| 128 | #103 | — | 52 | 1 | no | — |
| 129 | #102 | — | 52 | 1 | no | — |
| 130 | C22⋊C8 | — | 52 | 1 | no | — |
| 131 | C2×C13 | — | 2 | 1 | no | — |
| 132 | C2×C13 | — | 2 | 1 | no | — |
| 133 | C2×C13 | #1345 | 1 | 1 | yes | characteristic |
| 134 | C2×C13 | #1402 | 1 | 1 | yes | characteristic |
| 135 | C2×C13 | #1405 | 1 | 1 | yes | characteristic |
| 136 | D13 | — | 16 | 1 | no | — |
| 137 | #41 | — | 52 | 1 | no | — |
| 138 | #41 | — | 52 | 1 | no | — |
| 139 | #41 | — | 52 | 1 | no | — |
| 140 | #41 | — | 52 | 1 | no | — |
| 141 | C2×Q8 | — | 26 | 1 | no | — |
| 142 | C2×D4 | — | 26 | 1 | no | — |
| 143 | C2×D4 | — | 52 | 1 | no | — |
| 144 | C2×D4 | — | 52 | 1 | no | — |
| 145 | C22×C4 | — | 2 | 1 | no | — |
| 146 | C22×C4 | — | 26 | 1 | no | — |
| 147 | C22×C4 | — | 26 | 1 | no | — |
| 148 | C22×C4 | — | 52 | 1 | no | — |
| 149 | C22×C4 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 150 | M16 | — | 4 | 1 | no | — |
| 151 | M16 | — | 4 | 1 | no | — |
| 152 | C2×C8 | — | 4 | 1 | no | — |
| 153 | C2×C8 | — | 52 | 2 | no | — |
| 154 | C2×C8 | — | 104 | 1 | no | — |
| 155 | C2×C8 | — | 104 | 1 | no | — |
| 156 | C2×C8 | — | 104 | 1 | no | — |
| 157 | C4⋊C4 | — | 4 | 1 | no | — |
| 158 | C4⋊C4 | — | 52 | 1 | no | — |
| 159 | C4⋊C4 | — | 52 | 1 | no | — |
| 160 | C4⋊C4 | — | 104 | 1 | no | — |
| 161 | C4⋊C4 | — | 104 | 1 | no | — |
| 162 | C22⋊C4 | — | 52 | 2 | no | — |
| 163 | C42 | — | 13 | 1 | no | — |
| 164 | C42 | — | 13 | 1 | no | — |
| 165 | C42 | — | 26 | 1 | no | — |
| 166 | C13 | #7417 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 167 | C23 | — | 52 | 1 | no | — |
| 168 | C23 | #88107 | 1 | 1 | yes | characteristic |
| 169 | Q8 | — | 52 | 1 | no | — |
| 170 | Q8 | — | 52 | 1 | no | — |
| 171 | D4 | — | 52 | 1 | no | — |
| 172 | D4 | — | 52 | 1 | no | — |
| 173 | D4 | — | 104 | 1 | no | — |
| 174 | D4 | — | 104 | 1 | no | — |
| 175 | D4 | — | 208 | 1 | no | — |
| 176 | C2×C4 | — | 2 | 1 | no | — |
| 177 | C2×C4 | — | 2 | 1 | no | — |
| 178 | C2×C4 | — | 4 | 1 | no | — |
| 179 | C2×C4 | — | 8 | 1 | no | — |
| 180 | C2×C4 | — | 26 | 1 | no | — |
| 181 | C2×C4 | — | 26 | 1 | no | — |
| 182 | C2×C4 | — | 26 | 1 | no | — |
| 183 | C2×C4 | — | 26 | 1 | no | — |
| 184 | C2×C4 | — | 26 | 1 | no | — |
| 185 | C2×C4 | — | 26 | 1 | no | — |
| 186 | C2×C4 | — | 52 | 1 | no | — |
| 187 | C2×C4 | — | 52 | 1 | no | — |
| 188 | C2×C4 | — | 104 | 1 | no | — |
| 189 | C2×C4 | — | 104 | 1 | no | — |
| 190 | C2×C4 | — | 104 | 1 | no | — |
| 191 | C2×C4 | #88115 | 1 | 1 | yes | characteristic |
| 192 | C2×C4 | #88118 | 1 | 1 | yes | characteristic |
| 193 | C8 | — | 8 | 1 | no | — |
| 194 | C8 | — | 104 | 2 | no | — |
| 195 | C8 | — | 208 | 1 | no | — |
| 196 | C22 | — | 2 | 1 | no | — |
| 197 | C22 | — | 2 | 1 | no | — |
| 198 | C22 | — | 104 | 1 | no | — |
| 199 | C22 | — | 104 | 1 | no | — |
| 200 | C22 | — | 104 | 1 | no | — |
| 201 | C22 | #11718228 | 1 | 1 | yes | characteristic |
| 202 | C22 | #11718236 | 1 | 1 | yes | characteristic |
| 203 | C22 | #11718240 | 1 | 1 | yes | characteristic |
| 204 | C4 | — | 2 | 1 | no | — |
| 205 | C4 | — | 2 | 1 | no | — |
| 206 | C4 | — | 8 | 1 | no | — |
| 207 | C4 | — | 26 | 1 | no | — |
| 208 | C4 | — | 26 | 1 | no | — |
| 209 | C4 | — | 26 | 1 | no | — |
| 210 | C4 | — | 26 | 1 | no | — |
| 211 | C4 | — | 104 | 1 | no | — |
| 212 | C4 | — | 104 | 1 | no | — |
| 213 | C2 | — | 2 | 1 | no | — |
| 214 | C2 | — | 2 | 1 | no | — |
| 215 | C2 | — | 208 | 1 | no | — |
| 216 | C2 | #13129819 | 1 | 1 | yes | characteristic |
| 217 | C2 | #13129956 | 1 | 1 | yes | characteristic |
| 218 | C2 | #13129962 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13129779 | C2 | semidirect |
| 2. #13129714 | C2 | semidirect |
| 166. C13 | #7417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13129779 | 2 |
| #13129714 | 2 |
| #13116061 | 2 |
| #7417 | 13 |