Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
488 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20287119 | C2 | semidirect |
| 2. #20276994 | C2 | semidirect |
| 3. #20276904 | C2 | semidirect |
| 4. #20276894 | C2 | semidirect |
| 5. #20276872 | C2 | semidirect |
| 6. #20276815 | C2 | semidirect |
| 7. #20276548 | C2 | semidirect |
| 8. #20276500 | C2 | semidirect |
| 9. C4×D16×C53 | C2 | semidirect |
| 140. C4×D16 | D53 | semidirect |
| 173. C53 | #33922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287119 | 2 |
| #20276994 | 2 |
| #20276904 | 2 |
| #20276894 | 2 |
| #20276872 | 2 |
| #20276815 | 2 |
| #20276548 | 2 |
| #20276500 | 2 |
| C4×D16×C53 | 2 |
| #33922 | 53 |