Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
434 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 19. #16811542 | C4 | semidirect |
| 26. #16810440 | C4 | semidirect |
| 27. #16810439 | C4 | semidirect |
| 28. #16810438 | C4 | semidirect |
| 29. C53×#362 | C4 | semidirect |
| 164. #6157 | #362 | direct (N × H) |
| 201. #362 | #6157 | direct (N × H) |
| 205. C53 | C4×#362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×#6157 | 2 |
| D53⋊#362 | 2 |
| M32×#6157 | 2 |
| #108×#6157 | 2 |
| #20289791 | 2 |
| #20289790 | 2 |
| #362×D53 | 2 |
| C4×#362 | 53 |