Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
356 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20275488 | C2 | semidirect |
| 5. #20273005 | C2 | semidirect |
| 6. #20272556 | C2 | semidirect |
| 7. C53×#1303 | C2 | semidirect |
| 16. #16810368 | C4 | semidirect |
| 17. #16810368 | C4 | semidirect |
| 18. #16810366 | C4 | semidirect |
| 19. #16810366 | C4 | semidirect |
| 169. #1303 | D53 | semidirect |
| 196. C53 | #9592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275633 | 2 |
| #20275488 | 2 |
| #20273362 | 2 |
| #20273165 | 2 |
| #20273005 | 2 |
| #20272556 | 2 |
| C53×#1303 | 2 |
| #9592 | 53 |