Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
312 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20276509 | C2 | semidirect |
| 5. #20274888 | C2 | semidirect |
| 6. #20272794 | C2 | semidirect |
| 7. C53×#2161 | C2 | semidirect |
| 134. #2161 | D53 | semidirect |
| 160. C53 | #13532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276509 | 2 |
| #20276444 | 2 |
| #20276442 | 2 |
| #20275606 | 2 |
| #20274888 | 2 |
| #20272794 | 2 |
| C53×#2161 | 2 |
| #13532 | 53 |