Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
458 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 1. #21462720 | C2 | semidirect |
| 2. #21461591 | C2 | semidirect |
| 5. #21460712 | C2 | semidirect |
| 6. #21460671 | C2 | semidirect |
| 25. #16840058 | C4 | semidirect |
| 26. #16840057 | C4 | semidirect |
| 27. #16839959 | C4 | semidirect |
| 32. C61×#460 | C4 | semidirect |
| 217. #460 | #6923 | semidirect |
| 236. C61 | #9164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462720 | 2 |
| #21461591 | 2 |
| #21461289 | 2 |
| #21461199 | 2 |
| #21460712 | 2 |
| #21460671 | 2 |
| #21455940 | 2 |
| #9164 | 61 |