Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
354 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21447605 | C2 | semidirect |
| 2. C2×#16839582 | C2 | semidirect |
| 6. #21446565 | C2 | semidirect |
| 7. C61×#1387 | C2 | semidirect |
| 147. #1387 | D61 | semidirect |
| 171. C61 | #13478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447605 | 2 |
| C2×#16839582 | 2 |
| C2×#16839574 | 2 |
| #21447536 | 2 |
| #21446683 | 2 |
| #21446565 | 2 |
| C61×#1387 | 2 |
| #13478 | 61 |