Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
428 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 105 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. #16810364 | C4 | semidirect |
| 205. C53 | #8913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277900 | 2 |
| #20275683 | 2 |
| #20274881 | 2 |
| C2×#16810364 | 2 |
| #20272597 | 2 |
| #20272596 | 2 |
| C53×#1847 | 2 |
| #8913 | 53 |