Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
574 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 117 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. #21454899 | C2 | semidirect |
| 3. #21445812 | C2 | semidirect |
| 6. #21443722 | C2 | semidirect |
| 7. C61×#1303 | C2 | semidirect |
| 182. #1303 | D61 | semidirect |
| 207. C61 | #9398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454899 | 2 |
| #21450821 | 2 |
| #21445812 | 2 |
| #21444488 | 2 |
| #21444486 | 2 |
| #21443722 | 2 |
| C61×#1303 | 2 |
| #9398 | 61 |