Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
254 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 72 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. #16810447 | C4 | semidirect |
| 20. #16810446 | C4 | semidirect |
| 21. #16810445 | C4 | semidirect |
| 22. C53×#365 | C4 | semidirect |
| 141. #365 | #6157 | semidirect |
| 144. C53 | #13117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290822 | 2 |
| #108×#6157 | 2 |
| #20289797 | 2 |
| #20289793 | 2 |
| #20289784 | 2 |
| #20289758 | 2 |
| #20276486 | 2 |
| #13117 | 53 |