Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
528 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 528 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. #20287727 | C2 | semidirect |
| 2. #20276978 | C2 | semidirect |
| 3. #20276976 | C2 | semidirect |
| 4. #20276776 | C2 | semidirect |
| 5. #20276770 | C2 | semidirect |
| 6. #20276749 | C2 | semidirect |
| 7. #20276623 | C2 | semidirect |
| 8. #20276578 | C2 | semidirect |
| 9. C4×D16×C53 | C2 | semidirect |
| 153. C4×D16 | D53 | semidirect |
| 184. C53 | #33970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287727 | 2 |
| #20276978 | 2 |
| #20276976 | 2 |
| #20276776 | 2 |
| #20276770 | 2 |
| #20276749 | 2 |
| #20276623 | 2 |
| #20276578 | 2 |
| C4×D16×C53 | 2 |
| #33970 | 53 |