Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
294 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 14. #16811464 | C4 | semidirect |
| 15. C8×#88324 | C4 | semidirect |
| 19. #16810345 | C4 | semidirect |
| 20. #16810345 | C4 | semidirect |
| 21. #16810344 | C4 | semidirect |
| 22. C53×#322 | C4 | semidirect |
| 137. #322 | #6157 | semidirect |
| 139. C53 | #8142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290433 | 2 |
| #20289919 | 2 |
| #20289540 | 2 |
| #20289538 | 2 |
| #20273006 | 2 |
| #8142 | 53 |