Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
304 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 9. C22⋊#11719910 | C4 | semidirect |
| 12. C2×#13133157 | C4 | semidirect |
| 15. C2×M32×C53 | C4 | semidirect |
| 129. C2×M32 | #6157 | semidirect |
| 139. C53 | #7202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊(C22⋊C16) | 2 |
| C8×C22⋊#6157 | 2 |
| #20276325 | 2 |
| #7202 | 53 |