Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20276514 | C2 | semidirect |
| 2. #20273478 | C2 | semidirect |
| 3. #20272676 | C2 | semidirect |
| 8. C4×#11719908 | C22 | semidirect |
| 9. #16810376 | C22 | semidirect |
| 145. C53 | #11661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276514 | 2 |
| #20273478 | 2 |
| #20272676 | 2 |
| C2×C4×D8×C53 | 2 |
| #11661 | 53 |