Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20285915 | C2 | semidirect |
| 2. #20284815 | C2 | semidirect |
| 4. #20273349 | C2 | semidirect |
| 5. #20273189 | C2 | semidirect |
| 6. #20273055 | C2 | semidirect |
| 7. C53×#1287 | C2 | semidirect |
| 196. #1287 | D53 | semidirect |
| 228. C53 | #10042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285915 | 2 |
| #20284815 | 2 |
| #20284716 | 2 |
| #20273349 | 2 |
| #20273189 | 2 |
| #20273055 | 2 |
| C53×#1287 | 2 |
| #10042 | 53 |