Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20283632 | C2 | semidirect |
| 2. C2×#16810436 | C2 | semidirect |
| 3. #20276443 | C2 | semidirect |
| 4. #20275626 | C2 | semidirect |
| 5. #20272819 | C2 | semidirect |
| 6. #20272800 | C2 | semidirect |
| 24. C2×SD32×C53 | C4 | semidirect |
| 25. C2×D16×C53 | C4 | semidirect |
| 183. C2×SD32 | Dic53 | semidirect |
| 184. C2×D16 | Dic53 | semidirect |
| 197. C53 | #13036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283632 | 2 |
| C2×#16810436 | 2 |
| #20276443 | 2 |
| #20275626 | 2 |
| #20272819 | 2 |
| #20272800 | 2 |
| C2×C53×#509 | 2 |
| #13036 | 53 |