Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
376 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #20273489 | C2 | semidirect |
| 5. #20272612 | C2 | semidirect |
| 6. #20272548 | C2 | semidirect |
| 7. C4×C4⋊C8×C53 | C2 | semidirect |
| 15. #16810370 | C4 | semidirect |
| 16. #16810366 | C4 | semidirect |
| 151. C4×C4⋊C8 | D53 | semidirect |
| 178. C53 | #9577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275543 | 2 |
| #20273489 | 2 |
| #20273365 | 2 |
| #20273113 | 2 |
| #20272612 | 2 |
| #20272548 | 2 |
| C4×C4⋊C8×C53 | 2 |
| #9577 | 53 |