Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
368 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 29. #95×C53 | C8 | semidirect |
| 172. C53 | #7122 | semidirect |
| 191. #95 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289553 | 2 |
| #20272972 | 2 |
| #7122 | 53 |