Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
634 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 15. C2×#13133151 | C4 | semidirect |
| 16. C2×#13133150 | C4 | semidirect |
| 19. C2×#107×C53 | C4 | semidirect |
| 183. C2×#107 | #6157 | semidirect |
| 188. C53 | #11365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290418 | 2 |
| #20290407 | 2 |
| #20290402 | 2 |
| #20290380 | 2 |
| C2×#107×D53 | 2 |
| #11365 | 53 |