Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
186 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 22 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 | #13129968 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #13114451 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11718356 | — | 2 | 2 | no | — |
| 4 | #11718356 | C4 | 1 | 1 | yes | characteristic, complemented |
| 5 | #11718356 | C22 | 1 | 1 | yes | characteristic |
| 6 | #11718225 | — | 2 | 2 | no | — |
| 7 | C82×C13 | C4 | 1 | 1 | yes | characteristic, complemented |
| 8 | C2×D104 | — | 4 | 1 | no | — |
| 9 | C2×D104 | — | 4 | 1 | no | — |
| 10 | C2×D104 | — | 4 | 4 | no | — |
| 11 | #88128 | — | 2 | 1 | no | — |
| 12 | #88128 | D4 | 1 | 2 | yes | — |
| 13 | #88107 | — | 4 | 2 | no | — |
| 14 | C4×C8×C13 | — | 2 | 1 | no | — |
| 15 | C4×C8×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 16 | #7529 | — | 13 | 1 | no | maximal, Sylow |
| 17 | C2×D52 | — | 2 | 2 | no | — |
| 18 | C2×D52 | — | 4 | 2 | no | — |
| 19 | C2×D52 | — | 4 | 2 | no | — |
| 20 | C2×D52 | — | 4 | 1 | no | — |
| 21 | C22⋊#261 | — | 8 | 2 | no | — |
| 22 | C2×C8×C13 | — | 2 | 2 | no | — |
| 23 | C2×C8×C13 | — | 2 | 1 | no | — |
| 24 | C42×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 25 | D104 | — | 8 | 2 | no | — |
| 26 | D104 | — | 8 | 2 | no | — |
| 27 | D104 | — | 8 | 8 | no | — |
| 28 | #1712 | — | 13 | 1 | no | — |
| 29 | #1408 | — | 13 | 2 | no | — |
| 30 | C22×D13 | — | 4 | 2 | no | — |
| 31 | C22×D13 | — | 8 | 1 | no | — |
| 32 | C2×#261 | — | 16 | 2 | no | — |
| 33 | C2×C4×C13 | — | 2 | 1 | no | — |
| 34 | C2×C4×C13 | #99 | 1 | 1 | yes | characteristic |
| 35 | D52 | — | 8 | 2 | no | — |
| 36 | D52 | — | 8 | 4 | no | — |
| 37 | D52 | — | 8 | 4 | no | — |
| 38 | D52 | — | 8 | 2 | no | — |
| 39 | C8×C13 | — | 2 | 4 | no | — |
| 40 | C8×C13 | — | 2 | 2 | no | — |
| 41 | #493 | — | 13 | 1 | no | — |
| 42 | #493 | — | 13 | 1 | no | — |
| 43 | #493 | — | 26 | 2 | no | — |
| 44 | #353 | — | 26 | 2 | no | — |
| 45 | C82 | #261 | 1 | 1 | yes | characteristic, complemented |
| 46 | C22×C13 | #353 | 1 | 1 | yes | characteristic |
| 47 | C2×D13 | — | 8 | 2 | no | — |
| 48 | C2×D13 | — | 16 | 2 | no | — |
| 49 | C2×D13 | — | 16 | 2 | no | — |
| 50 | C2×D13 | — | 16 | 1 | no | — |
| 51 | #261 | — | 32 | 2 | no | — |
| 52 | C4×C13 | — | 2 | 2 | no | — |
| 53 | C4×C13 | — | 2 | 1 | no | — |
| 54 | C2×D8 | — | 52 | 1 | no | — |
| 55 | C2×D8 | — | 52 | 1 | no | — |
| 56 | C2×D8 | — | 52 | 4 | no | — |
| 57 | #127 | — | 13 | 2 | no | — |
| 58 | #127 | — | 26 | 1 | no | — |
| 59 | #99 | — | 52 | 2 | no | — |
| 60 | C4×C8 | — | 2 | 1 | no | — |
| 61 | C4×C8 | C2×#261 | 1 | 1 | yes | characteristic |
| 62 | C2×C13 | — | 2 | 1 | no | — |
| 63 | C2×C13 | #1408 | 1 | 1 | yes | characteristic |
| 64 | D13 | — | 16 | 2 | no | — |
| 65 | D13 | — | 32 | 1 | no | — |
| 66 | C2×D4 | — | 26 | 2 | no | — |
| 67 | C2×D4 | — | 52 | 2 | no | — |
| 68 | C2×D4 | — | 52 | 2 | no | — |
| 69 | C2×D4 | — | 52 | 1 | no | — |
| 70 | D8 | — | 104 | 2 | no | — |
| 71 | D8 | — | 104 | 2 | no | — |
| 72 | D8 | — | 104 | 8 | no | — |
| 73 | C2×C8 | — | 2 | 2 | no | — |
| 74 | C2×C8 | — | 2 | 1 | no | — |
| 75 | C22⋊C4 | — | 104 | 2 | no | — |
| 76 | C42 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 77 | C13 | #7529 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 78 | C23 | — | 52 | 2 | no | — |
| 79 | C23 | — | 104 | 1 | no | — |
| 80 | D4 | — | 104 | 2 | no | — |
| 81 | D4 | — | 104 | 4 | no | — |
| 82 | D4 | — | 104 | 4 | no | — |
| 83 | D4 | — | 104 | 2 | no | — |
| 84 | C2×C4 | — | 2 | 1 | no | — |
| 85 | C2×C4 | — | 208 | 2 | no | — |
| 86 | C2×C4 | #88107 | 1 | 1 | yes | characteristic |
| 87 | C8 | — | 2 | 4 | no | — |
| 88 | C8 | — | 2 | 2 | no | — |
| 89 | C22 | — | 104 | 2 | no | — |
| 90 | C22 | — | 208 | 2 | no | — |
| 91 | C22 | — | 208 | 2 | no | — |
| 92 | C22 | — | 208 | 1 | no | — |
| 93 | C22 | #11718225 | 1 | 1 | yes | characteristic |
| 94 | C4 | — | 2 | 2 | no | — |
| 95 | C4 | — | 2 | 1 | no | — |
| 96 | C4 | — | 416 | 2 | no | — |
| 97 | C2 | — | 2 | 1 | no | — |
| 98 | C2 | — | 416 | 1 | no | — |
| 99 | C2 | — | 208 | 2 | no | — |
| 100 | C2 | #13129968 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13129968 | C2 | semidirect |
| 4. #11718356 | C4 | semidirect |
| 7. C82×C13 | C4 | semidirect |
| 45. C82 | #261 | semidirect |
| 77. C13 | #7529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13129968 | 2 |
| #13114451 | 2 |
| #7529 | 13 |