Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 498 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 |
|---|---|---|
| 4. #20272563 | C2 | semidirect |
| 5. #20272562 | C2 | semidirect |
| 6. #20272561 | C2 | semidirect |
| 7. C53×#1282 | C2 | semidirect |
| 236. #1282 | D53 | semidirect |
| 267. C53 | #8736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277310 | 2 |
| C2×#16810346 | 2 |
| #20272563 | 2 |
| #20272562 | 2 |
| #20272561 | 2 |
| C53×#1282 | 2 |
| #8736 | 53 |