Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20276488 | C2 | semidirect |
| 3. #20276487 | C2 | semidirect |
| 6. #20272829 | C2 | semidirect |
| 7. C53×#1389 | C2 | semidirect |
| 19. #16810404 | C4 | semidirect |
| 41. #13133157 | C2×C4 | semidirect |
| 54. M32×C53 | C2×C4 | semidirect |
| 150. #1389 | D53 | semidirect |
| 172. C53 | #12932 | semidirect |
| 195. M32 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283303 | 2 |
| #20276488 | 2 |
| #20276487 | 2 |
| C2×#16810404 | 2 |
| #20274754 | 2 |
| #20272829 | 2 |
| C53×#1389 | 2 |
| #12932 | 53 |