Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
318 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 318 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 |
|---|---|---|
| 16. #16810371 | C4 | semidirect |
| 17. #16810371 | C4 | semidirect |
| 18. #16810370 | C4 | semidirect |
| 19. #16810370 | C4 | semidirect |
| 179. C53 | #9591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275658 | 2 |
| #20275488 | 2 |
| #20273370 | 2 |
| #20273169 | 2 |
| #20273005 | 2 |
| #20272556 | 2 |
| C53×#1303 | 2 |
| #9591 | 53 |