Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 24. C2×Q32×C53 | C4 | semidirect |
| 167. C2×Q32 | Dic53 | semidirect |
| 180. C53 | #13020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283583 | 2 |
| C2×#16810439 | 2 |
| #20276435 | 2 |
| #20275631 | 2 |
| #20272811 | 2 |
| #20272803 | 2 |
| C22×Q32×C53 | 2 |
| #13020 | 53 |