Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
232 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×#16810463 | C2 | semidirect |
| 5. #20276966 | C2 | semidirect |
| 6. #20272848 | C2 | semidirect |
| 7. C2×C53×Q64 | C2 | semidirect |
| 96. C2×Q64 | D53 | semidirect |
| 120. C53 | #13730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810463 | 2 |
| C2×#16810462 | 2 |
| C2×#16810460 | 2 |
| #20276977 | 2 |
| #20276966 | 2 |
| #20272848 | 2 |
| C2×C53×Q64 | 2 |
| #13730 | 53 |