Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
358 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 138 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. #14519848 | C8 | semidirect |
| 123. C61 | #8294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519848 | 2 |
| #21461367 | 2 |
| C8×#11758213 | 2 |
| #21460651 | 2 |
| #322×D61 | 2 |
| #8294 | 61 |