Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
656 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #13131019 | C2 | 1 | 3 | yes | maximal |
| 2 | D13⋊#330 | C2 | 1 | 3 | yes | maximal |
| 3 | D13×#564 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C13×#564 | C4 | 1 | 1 | yes | characteristic, complemented |
| 5 | D13×#125 | — | 2 | 6 | no | — |
| 6 | D13×#125 | C22 | 1 | 3 | yes | — |
| 7 | C13⋊#564 | — | 2 | 6 | no | — |
| 8 | C13⋊#564 | C4 | 1 | 3 | yes | complemented |
| 9 | #11719059 | C22 | 1 | 1 | yes | characteristic |
| 10 | #11719047 | C22 | 1 | 3 | yes | — |
| 11 | #11718246 | — | 2 | 6 | no | — |
| 12 | #11718242 | — | 2 | 6 | no | — |
| 13 | C2×C4⋊#261 | — | 2 | 3 | no | — |
| 14 | C2×D13⋊C8 | — | 2 | 3 | no | — |
| 15 | C13×#125 | — | 2 | 6 | no | — |
| 16 | C13×#125 | C2×C4 | 1 | 3 | yes | — |
| 17 | C4⋊C4×D13 | — | 2 | 6 | no | — |
| 18 | C4⋊C4×D13 | — | 2 | 6 | no | — |
| 19 | C4⋊C4×D13 | D4 | 1 | 6 | yes | — |
| 20 | #88144 | — | 2 | 6 | no | — |
| 21 | #88144 | — | 2 | 6 | no | — |
| 22 | #88144 | D4 | 1 | 6 | yes | — |
| 23 | #88143 | — | 2 | 6 | no | — |
| 24 | #88143 | — | 2 | 6 | no | — |
| 25 | #88143 | — | 2 | 6 | no | — |
| 26 | #88143 | — | 2 | 6 | no | — |
| 27 | #88143 | — | 2 | 6 | no | — |
| 28 | C42×D13 | — | 2 | 2 | no | — |
| 29 | C42×D13 | C23 | 1 | 1 | yes | characteristic |
| 30 | #88124 | — | 2 | 6 | no | — |
| 31 | #88124 | C2×C4 | 1 | 3 | yes | — |
| 32 | #88110 | — | 2 | 6 | no | — |
| 33 | #8509 | — | 13 | 1 | no | maximal, Sylow |
| 34 | C22×#261 | — | 4 | 1 | no | — |
| 35 | C2×C4×D13 | — | 2 | 6 | no | — |
| 36 | C2×C4×D13 | C2×D4 | 1 | 3 | yes | — |
| 37 | C2×#1057 | — | 4 | 3 | no | — |
| 38 | C4⋊#261 | — | 4 | 6 | no | — |
| 39 | D13⋊C8 | — | 2 | 6 | no | — |
| 40 | D13⋊C8 | — | 4 | 3 | no | — |
| 41 | C13×C4⋊C4 | — | 2 | 6 | no | — |
| 42 | C13×C4⋊C4 | — | 2 | 6 | no | — |
| 43 | C13×C4⋊C4 | C22⋊C4 | 1 | 6 | yes | — |
| 44 | C42×C13 | — | 2 | 2 | no | — |
| 45 | C42×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 46 | C4⋊Dic13 | — | 2 | 6 | no | — |
| 47 | C4⋊Dic13 | — | 2 | 6 | no | — |
| 48 | C4⋊Dic13 | C22⋊C4 | 1 | 6 | yes | — |
| 49 | #6101 | — | 2 | 6 | no | — |
| 50 | #6101 | — | 2 | 6 | no | — |
| 51 | #6101 | — | 2 | 6 | no | — |
| 52 | #6101 | — | 2 | 6 | no | — |
| 53 | #6101 | — | 2 | 6 | no | — |
| 54 | C4×Dic13 | — | 2 | 6 | no | — |
| 55 | C4×Dic13 | C2×D4 | 1 | 3 | yes | — |
| 56 | C2×#564 | — | 13 | 1 | no | — |
| 57 | #1992 | — | 13 | 3 | no | — |
| 58 | C2×#330 | — | 13 | 3 | no | — |
| 59 | C22×D13 | #120 | 1 | 1 | yes | characteristic |
| 60 | C2×#261 | — | 8 | 3 | no | — |
| 61 | C2×C4×C13 | — | 2 | 6 | no | — |
| 62 | C2×C4×C13 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 63 | C2×Dic13 | — | 2 | 6 | no | — |
| 64 | C2×Dic13 | #120 | 1 | 3 | yes | — |
| 65 | C4×D13 | — | 2 | 3 | no | — |
| 66 | C4×D13 | — | 2 | 3 | no | — |
| 67 | C4×D13 | — | 4 | 6 | no | — |
| 68 | C4×D13 | — | 4 | 6 | no | — |
| 69 | #1057 | — | 4 | 6 | no | — |
| 70 | #564 | — | 13 | 3 | no | — |
| 71 | #564 | — | 26 | 6 | no | — |
| 72 | #564 | #261 | 1 | 1 | yes | characteristic, complemented |
| 73 | C2×#125 | — | 13 | 3 | no | — |
| 74 | C2×#125 | — | 26 | 6 | no | — |
| 75 | C2×#97 | — | 13 | 3 | no | — |
| 76 | #384 | — | 13 | 1 | no | — |
| 77 | #340 | — | 26 | 6 | no | — |
| 78 | #330 | — | 26 | 6 | no | — |
| 79 | C22×C13 | #379 | 1 | 1 | yes | characteristic |
| 80 | C2×D13 | #454 | 1 | 3 | yes | — |
| 81 | C2×D13 | #456 | 1 | 3 | yes | — |
| 82 | #261 | — | 16 | 1 | no | — |
| 83 | C4×C13 | — | 2 | 3 | no | — |
| 84 | C4×C13 | — | 4 | 6 | no | — |
| 85 | Dic13 | — | 2 | 3 | no | — |
| 86 | Dic13 | — | 4 | 6 | no | — |
| 87 | C22×C8 | — | 26 | 3 | no | — |
| 88 | #125 | — | 2 | 6 | no | — |
| 89 | #125 | — | 13 | 6 | no | — |
| 90 | #125 | — | 13 | 3 | no | — |
| 91 | #125 | — | 26 | 6 | no | — |
| 92 | #125 | — | 26 | 6 | no | — |
| 93 | #125 | — | 26 | 6 | no | — |
| 94 | #125 | — | 26 | 6 | no | — |
| 95 | #125 | — | 26 | 6 | no | — |
| 96 | #125 | — | 26 | 6 | no | — |
| 97 | #125 | — | 26 | 6 | no | — |
| 98 | #125 | — | 26 | 6 | no | — |
| 99 | #125 | C2×#261 | 1 | 3 | yes | — |
| 100 | C2×C4⋊C4 | — | 13 | 6 | no | — |
| 101 | C2×C4⋊C4 | — | 26 | 6 | no | — |
| 102 | C2×C4⋊C4 | — | 26 | 6 | no | — |
| 103 | C2×C4⋊C4 | — | 26 | 3 | no | — |
| 104 | C2×C42 | — | 13 | 1 | no | — |
| 105 | C2×C42 | — | 26 | 2 | no | — |
| 106 | #97 | — | 26 | 6 | no | — |
| 107 | C2×C13 | #1793 | 1 | 3 | yes | — |
| 108 | D13 | #1658 | 1 | 1 | yes | characteristic |
| 109 | D13 | #1663 | 1 | 3 | yes | — |
| 110 | C22×C4 | — | 13 | 3 | no | — |
| 111 | C22×C4 | — | 26 | 6 | no | — |
| 112 | C22×C4 | — | 52 | 1 | no | — |
| 113 | C2×C8 | — | 26 | 6 | no | — |
| 114 | C2×C8 | — | 52 | 3 | no | — |
| 115 | C2×C8 | — | 52 | 3 | no | — |
| 116 | C4⋊C4 | — | 2 | 6 | no | — |
| 117 | C4⋊C4 | — | 2 | 6 | no | — |
| 118 | C4⋊C4 | — | 13 | 6 | no | — |
| 119 | C4⋊C4 | — | 26 | 6 | no | — |
| 120 | C4⋊C4 | — | 26 | 6 | no | — |
| 121 | C4⋊C4 | — | 26 | 6 | no | — |
| 122 | C4⋊C4 | — | 26 | 6 | no | — |
| 123 | C4⋊C4 | — | 26 | 6 | no | — |
| 124 | C4⋊C4 | — | 26 | 6 | no | — |
| 125 | C4⋊C4 | — | 26 | 6 | no | — |
| 126 | C4⋊C4 | — | 52 | 6 | no | — |
| 127 | C4⋊C4 | C22⋊#261 | 1 | 6 | yes | — |
| 128 | C42 | — | 2 | 2 | no | — |
| 129 | C42 | — | 13 | 3 | no | — |
| 130 | C42 | — | 26 | 6 | no | — |
| 131 | C42 | C22×#261 | 1 | 1 | yes | characteristic |
| 132 | C13 | #8509 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 133 | C23 | — | 13 | 1 | no | — |
| 134 | C2×C4 | — | 2 | 6 | no | — |
| 135 | C2×C4 | — | 13 | 3 | no | — |
| 136 | C2×C4 | — | 26 | 3 | no | — |
| 137 | C2×C4 | — | 26 | 3 | no | — |
| 138 | C2×C4 | — | 26 | 6 | no | — |
| 139 | C2×C4 | — | 52 | 6 | no | — |
| 140 | C2×C4 | — | 52 | 6 | no | — |
| 141 | C2×C4 | — | 104 | 3 | no | — |
| 142 | C2×C4 | C2×C22⋊#261 | 1 | 3 | yes | — |
| 143 | C8 | — | 52 | 6 | no | — |
| 144 | C22 | — | 13 | 3 | no | — |
| 145 | C22 | — | 13 | 3 | no | — |
| 146 | C22 | #11719171 | 1 | 1 | yes | characteristic |
| 147 | C4 | — | 2 | 3 | no | — |
| 148 | C4 | — | 4 | 6 | no | — |
| 149 | C4 | — | 26 | 3 | no | — |
| 150 | C4 | — | 52 | 6 | no | — |
| 151 | C4 | — | 208 | 1 | no | — |
| 152 | C2 | — | 13 | 1 | no | — |
| 153 | C2 | — | 13 | 3 | no | — |
| 154 | C2 | #13130683 | 1 | 3 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C13×#564 | C4 | semidirect |
| 8. C13⋊#564 | C4 | semidirect |
| 72. #564 | #261 | semidirect |
| 132. C13 | #8509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131019 | 2 |
| D13⋊#330 | 2 |
| D13×#564 | 2 |
| #8509 | 13 |