Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
366 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 100 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. #16810753 | C4 | semidirect |
| 17. Q8×#88322 | C4 | semidirect |
| 19. #16810747 | C4 | semidirect |
| 24. C53×#446 | C4 | semidirect |
| 163. #446 | #6157 | semidirect |
| 179. C53 | #8675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290652 | 2 |
| #20290265 | 2 |
| #20290148 | 2 |
| #20289570 | 2 |
| #20283646 | 2 |
| #8675 | 53 |