Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 22. #16810365 | C4 | semidirect |
| 202. C53 | #8912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277901 | 2 |
| #20274881 | 2 |
| #20274850 | 2 |
| C2×#16810365 | 2 |
| #20272597 | 2 |
| C53×#1992 | 2 |
| #8912 | 53 |