Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
432 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 24. #16840142 | C4 | semidirect |
| 25. #16840114 | C4 | semidirect |
| 26. #16840114 | C4 | semidirect |
| 30. C61×#500 | C4 | semidirect |
| 94. #11758213 | Q16 | semidirect |
| 189. #500 | #6923 | semidirect |
| 210. C61 | #9056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462613 | 2 |
| #21461995 | 2 |
| #21461202 | 2 |
| #21461128 | 2 |
| #21460654 | 2 |
| #21460651 | 2 |
| #21456406 | 2 |
| #9056 | 61 |