Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
508 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 90 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. #20290944 | C2 | semidirect |
| 2. #20290401 | C2 | semidirect |
| 3. #20289701 | C2 | semidirect |
| 8. #16811518 | C22 | semidirect |
| 10. #16811497 | C22 | semidirect |
| 15. #16810856 | C4 | semidirect |
| 17. C2×#13133151 | C4 | semidirect |
| 19. C22×D8×C53 | C4 | semidirect |
| 161. C22×D8 | #6157 | semidirect |
| 176. C53 | #11705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290944 | 2 |
| #20290401 | 2 |
| #20289701 | 2 |
| C2×#16810856 | 2 |
| #11705 | 53 |