Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
930 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 159 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. #20276451 | C2 | semidirect |
| 2. #20276431 | C2 | semidirect |
| 3. #20276336 | C2 | semidirect |
| 4. #20274761 | C2 | semidirect |
| 6. C2×#13133157 | C22 | semidirect |
| 7. #16810661 | C22 | semidirect |
| 18. C2×#135×C53 | C4 | semidirect |
| 20. C22×D8×C53 | C4 | semidirect |
| 185. C2×#135 | Dic53 | semidirect |
| 187. C22×D8 | Dic53 | semidirect |
| 197. C53 | #12741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276451 | 2 |
| #20276431 | 2 |
| #20276336 | 2 |
| #20274761 | 2 |
| C2×C53×#576 | 2 |
| #12741 | 53 |