Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
464 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 18. #16810421 | C4 | semidirect |
| 190. C53 | #12631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277431 | 2 |
| C2×#16810421 | 2 |
| C4×#13133136 | 2 |
| #20272841 | 2 |
| C4×#101×C53 | 2 |
| #12631 | 53 |