Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#16811549 | C2 | semidirect |
| 4. #20290833 | C2 | semidirect |
| 5. #20289791 | C2 | semidirect |
| 6. #20289768 | C2 | semidirect |
| 25. #16810431 | C4 | semidirect |
| 26. #16810430 | C4 | semidirect |
| 27. #16810429 | C4 | semidirect |
| 28. C53×#359 | C4 | semidirect |
| 62. C2×#11719908 | C2×C4 | semidirect |
| 65. #13133153 | C2×C4 | semidirect |
| 68. C2×C16×C53 | C2×C4 | semidirect |
| 69. #108×C53 | C2×C4 | semidirect |
| 209. #359 | #6157 | semidirect |
| 213. C53 | #12945 | semidirect |
| 241. C2×C16 | C2×#6157 | semidirect |
| 244. #108 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291477 | 2 |
| C2×#16811549 | 2 |
| #20291023 | 2 |
| #20290833 | 2 |
| #20289791 | 2 |
| #20289768 | 2 |
| #359×D53 | 2 |
| #12945 | 53 |