Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
234 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 32 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 | #13129927 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13129771 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13115958 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×#88163 | — | 2 | 1 | no | — |
| 5 | C22×Dic52 | C4 | 1 | 1 | yes | characteristic |
| 6 | #11719132 | — | 2 | 1 | no | — |
| 7 | C2×#88064 | — | 2 | 1 | no | — |
| 8 | #11718771 | C22 | 1 | 1 | yes | characteristic |
| 9 | #11718284 | — | 2 | 1 | no | — |
| 10 | C13×#341 | C4 | 1 | 1 | yes | characteristic |
| 11 | C2×#6127 | D4 | 1 | 1 | yes | characteristic |
| 12 | C22×Dic26 | — | 2 | 1 | no | — |
| 13 | D13⋊M16 | — | 4 | 1 | no | — |
| 14 | C2×C13×M16 | — | 2 | 1 | no | — |
| 15 | C22×C8×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 16 | C2×#6099 | D4 | 1 | 1 | yes | characteristic |
| 17 | #88163 | — | 4 | 2 | no | — |
| 18 | #88163 | — | 4 | 2 | no | — |
| 19 | C2×Dic52 | — | 4 | 1 | no | — |
| 20 | C2×Dic52 | — | 4 | 1 | no | — |
| 21 | C2×Dic52 | — | 4 | 2 | no | — |
| 22 | C2×#6095 | — | 4 | 1 | no | — |
| 23 | #88121 | — | 2 | 2 | no | — |
| 24 | #88113 | — | 4 | 1 | no | — |
| 25 | #88106 | — | 4 | 1 | no | — |
| 26 | #88064 | — | 4 | 2 | no | — |
| 27 | #88060 | — | 4 | 1 | no | — |
| 28 | #7401 | — | 13 | 1 | no | maximal, Sylow |
| 29 | C22×C4×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 30 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 31 | C22×Dic13 | — | 4 | 1 | no | — |
| 32 | #6127 | — | 4 | 1 | no | — |
| 33 | #6127 | — | 4 | 1 | no | — |
| 34 | C2×D52 | SD16 | 1 | 1 | yes | characteristic |
| 35 | C2×C4×D13 | — | 2 | 1 | no | — |
| 36 | C2×Dic26 | — | 2 | 2 | no | — |
| 37 | C2×Dic26 | — | 4 | 1 | no | — |
| 38 | C2×Dic26 | — | 4 | 1 | no | — |
| 39 | C2×Dic26 | — | 4 | 1 | no | — |
| 40 | C2×Dic26 | — | 4 | 1 | no | — |
| 41 | C2×Dic26 | — | 4 | 1 | no | — |
| 42 | C2×Dic26 | D8 | 1 | 1 | yes | characteristic |
| 43 | #6122 | — | 4 | 2 | no | — |
| 44 | #6118 | — | 8 | 1 | no | — |
| 45 | D13⋊C8 | — | 8 | 1 | no | — |
| 46 | C13×M16 | — | 2 | 2 | no | — |
| 47 | C13×M16 | — | 4 | 1 | no | — |
| 48 | C2×C8×C13 | — | 2 | 1 | no | — |
| 49 | C2×C8×C13 | — | 4 | 1 | no | — |
| 50 | C2×C8×C13 | — | 4 | 1 | no | — |
| 51 | #6099 | — | 4 | 1 | no | — |
| 52 | C2×#1055 | — | 2 | 1 | no | — |
| 53 | Dic52 | — | 4 | 2 | no | — |
| 54 | Dic52 | — | 4 | 4 | no | — |
| 55 | Dic52 | — | 4 | 2 | no | — |
| 56 | #6095 | — | 4 | 4 | no | — |
| 57 | #6092 | — | 8 | 1 | no | — |
| 58 | #2020 | — | 13 | 1 | no | — |
| 59 | #1392 | — | 13 | 1 | no | — |
| 60 | #1321 | — | 13 | 1 | no | — |
| 61 | C23×C13 | #104 | 1 | 1 | yes | characteristic |
| 62 | C22×D13 | — | 2 | 1 | no | — |
| 63 | C2×C4×C13 | — | 2 | 1 | no | — |
| 64 | C2×C4×C13 | — | 2 | 1 | no | — |
| 65 | C2×C4×C13 | #99 | 1 | 1 | yes | characteristic |
| 66 | C2×C4×C13 | #102 | 1 | 1 | yes | characteristic |
| 67 | C22⋊D13 | — | 8 | 1 | no | — |
| 68 | C2×Dic13 | — | 2 | 1 | no | — |
| 69 | C2×Dic13 | — | 4 | 2 | no | — |
| 70 | C2×Dic13 | — | 8 | 1 | no | — |
| 71 | C2×Dic13 | — | 8 | 1 | no | — |
| 72 | D52 | — | 4 | 1 | no | — |
| 73 | C4×D13 | — | 4 | 1 | no | — |
| 74 | C4×D13 | — | 4 | 1 | no | — |
| 75 | Dic26 | — | 4 | 1 | no | — |
| 76 | Dic26 | — | 4 | 2 | no | — |
| 77 | Dic26 | — | 4 | 2 | no | — |
| 78 | Dic26 | — | 8 | 1 | no | — |
| 79 | Dic26 | — | 8 | 1 | no | — |
| 80 | #1057 | — | 8 | 2 | no | — |
| 81 | C8×C13 | — | 4 | 2 | no | — |
| 82 | C8×C13 | — | 4 | 1 | no | — |
| 83 | #1055 | — | 4 | 1 | no | — |
| 84 | C2×#137 | — | 26 | 1 | no | — |
| 85 | C22×Q16 | — | 13 | 1 | no | — |
| 86 | #413 | — | 26 | 1 | no | — |
| 87 | C2×#101 | — | 26 | 1 | no | — |
| 88 | #408 | — | 13 | 1 | no | — |
| 89 | #349 | — | 26 | 1 | no | — |
| 90 | #341 | #261 | 1 | 1 | yes | characteristic |
| 91 | C22×C13 | — | 2 | 1 | no | — |
| 92 | C22×C13 | — | 4 | 1 | no | — |
| 93 | C22×C13 | #327 | 1 | 1 | yes | characteristic |
| 94 | C2×D13 | — | 4 | 1 | no | — |
| 95 | C2×D13 | — | 8 | 1 | no | — |
| 96 | C4×C13 | — | 2 | 1 | no | — |
| 97 | C4×C13 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 98 | C4×C13 | #353 | 1 | 1 | yes | characteristic |
| 99 | Dic13 | — | 4 | 1 | no | — |
| 100 | Dic13 | — | 8 | 2 | no | — |
| 101 | C2×#41 | — | 13 | 1 | no | — |
| 102 | C22×Q8 | — | 26 | 1 | no | — |
| 103 | #137 | — | 52 | 2 | no | — |
| 104 | #137 | — | 52 | 2 | no | — |
| 105 | C2×Q16 | — | 52 | 1 | no | — |
| 106 | C2×Q16 | — | 52 | 1 | no | — |
| 107 | C2×Q16 | — | 52 | 2 | no | — |
| 108 | C2×SD16 | — | 52 | 1 | no | — |
| 109 | C2×M16 | — | 2 | 1 | no | — |
| 110 | C2×M16 | — | 13 | 1 | no | — |
| 111 | C2×M16 | — | 52 | 1 | no | — |
| 112 | C22×C8 | C2×#261 | 1 | 1 | yes | characteristic |
| 113 | M32 | — | 52 | 1 | no | — |
| 114 | #101 | — | 52 | 2 | no | — |
| 115 | #101 | — | 52 | 1 | no | — |
| 116 | #100 | — | 26 | 2 | no | — |
| 117 | C22⋊C8 | — | 52 | 1 | no | — |
| 118 | C2×C13 | — | 2 | 1 | no | — |
| 119 | C2×C13 | — | 4 | 1 | no | — |
| 120 | C2×C13 | #1343 | 1 | 1 | yes | characteristic |
| 121 | D13 | — | 8 | 1 | no | — |
| 122 | #41 | — | 52 | 1 | no | — |
| 123 | #41 | — | 52 | 1 | no | — |
| 124 | C2×Q8 | — | 13 | 1 | no | — |
| 125 | C2×Q8 | — | 26 | 2 | no | — |
| 126 | C2×Q8 | — | 52 | 1 | no | — |
| 127 | C2×Q8 | — | 52 | 1 | no | — |
| 128 | C2×Q8 | — | 52 | 1 | no | — |
| 129 | C2×Q8 | — | 52 | 1 | no | — |
| 130 | C2×Q8 | — | 52 | 1 | no | — |
| 131 | C2×D4 | — | 13 | 1 | no | — |
| 132 | C2×D4 | — | 26 | 1 | no | — |
| 133 | C22×C4 | — | 26 | 1 | no | — |
| 134 | C22×C4 | — | 52 | 1 | no | — |
| 135 | C22×C4 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 136 | Q16 | — | 52 | 2 | no | — |
| 137 | Q16 | — | 52 | 2 | no | — |
| 138 | Q16 | — | 52 | 4 | no | — |
| 139 | SD16 | — | 52 | 4 | no | — |
| 140 | M16 | — | 2 | 2 | no | — |
| 141 | M16 | — | 4 | 1 | no | — |
| 142 | M16 | — | 52 | 1 | no | — |
| 143 | M16 | — | 52 | 2 | no | — |
| 144 | M16 | — | 104 | 1 | no | — |
| 145 | C2×C8 | — | 2 | 1 | no | — |
| 146 | C2×C8 | — | 4 | 1 | no | — |
| 147 | C2×C8 | — | 4 | 1 | no | — |
| 148 | C2×C8 | — | 26 | 1 | no | — |
| 149 | C2×C8 | — | 104 | 1 | no | — |
| 150 | C16 | — | 104 | 1 | no | — |
| 151 | C13 | #7401 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 152 | C23 | — | 26 | 1 | no | — |
| 153 | C23 | #88118 | 1 | 1 | yes | characteristic |
| 154 | Q8 | — | 52 | 1 | no | — |
| 155 | Q8 | — | 52 | 2 | no | — |
| 156 | Q8 | — | 52 | 2 | no | — |
| 157 | Q8 | — | 104 | 1 | no | — |
| 158 | Q8 | — | 104 | 1 | no | — |
| 159 | D4 | — | 52 | 1 | no | — |
| 160 | D4 | — | 104 | 1 | no | — |
| 161 | C2×C4 | — | 2 | 1 | no | — |
| 162 | C2×C4 | — | 2 | 1 | no | — |
| 163 | C2×C4 | — | 26 | 1 | no | — |
| 164 | C2×C4 | — | 52 | 1 | no | — |
| 165 | C2×C4 | — | 52 | 1 | no | — |
| 166 | C2×C4 | — | 52 | 2 | no | — |
| 167 | C2×C4 | — | 104 | 1 | no | — |
| 168 | C2×C4 | — | 104 | 1 | no | — |
| 169 | C2×C4 | #88107 | 1 | 1 | yes | characteristic |
| 170 | C2×C4 | #88115 | 1 | 1 | yes | characteristic |
| 171 | C8 | — | 4 | 2 | no | — |
| 172 | C8 | — | 4 | 1 | no | — |
| 173 | C8 | — | 52 | 1 | no | — |
| 174 | C8 | — | 104 | 2 | no | — |
| 175 | C22 | — | 2 | 1 | no | — |
| 176 | C22 | — | 4 | 1 | no | — |
| 177 | C22 | — | 52 | 1 | no | — |
| 178 | C22 | — | 104 | 1 | no | — |
| 179 | C22 | #11718240 | 1 | 1 | yes | characteristic |
| 180 | C4 | — | 2 | 1 | no | — |
| 181 | C4 | — | 52 | 1 | no | — |
| 182 | C4 | — | 104 | 2 | no | — |
| 183 | C4 | #11718225 | 1 | 1 | yes | characteristic |
| 184 | C4 | #11718236 | 1 | 1 | yes | characteristic |
| 185 | C2 | — | 2 | 1 | no | — |
| 186 | C2 | — | 4 | 1 | no | — |
| 187 | C2 | — | 104 | 1 | no | — |
| 188 | C2 | #13129815 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 151. C13 | #7401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13129927 | 2 |
| #13129771 | 2 |
| #13115958 | 2 |
| #7401 | 13 |