Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
384 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 88 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. C4×#13133285 | C2 | semidirect |
| 2. #20290276 | C2 | semidirect |
| 4. #20289567 | C2 | semidirect |
| 15. Q8×#88322 | C4 | semidirect |
| 16. #16810702 | C4 | semidirect |
| 19. #16810688 | C4 | semidirect |
| 24. C53×#446 | C4 | semidirect |
| 159. #446 | #6157 | semidirect |
| 177. C53 | #8696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133285 | 2 |
| #20290276 | 2 |
| #20290119 | 2 |
| #20289567 | 2 |
| #20283689 | 2 |
| #8696 | 53 |