Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 1. #20290637 | C2 | semidirect |
| 2. #20290265 | C2 | semidirect |
| 4. #20289570 | C2 | semidirect |
| 16. #16810701 | C4 | semidirect |
| 17. #16810700 | C4 | semidirect |
| 19. C8×D212 | C4 | semidirect |
| 24. C8×D4×C53 | C4 | semidirect |
| 178. C8×D4 | #6157 | semidirect |
| 190. C53 | #8680 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290637 | 2 |
| #20290265 | 2 |
| #20290145 | 2 |
| #20289570 | 2 |
| #20283422 | 2 |
| #8680 | 53 |