Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
578 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 578 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 |
|---|---|---|
| 3. C2×#16810427 | C2 | semidirect |
| 5. #20275577 | C2 | semidirect |
| 6. #20272792 | C2 | semidirect |
| 7. C22×Q32×C53 | C2 | semidirect |
| 186. C22×Q32 | D53 | semidirect |
| 220. C53 | #13329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133160 | 2 |
| C2×#16811008 | 2 |
| C2×#16810427 | 2 |
| C2×#16810425 | 2 |
| #20275577 | 2 |
| #20272792 | 2 |
| C22×Q32×C53 | 2 |
| #13329 | 53 |