Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
378 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21456355 | C2 | semidirect |
| 5. #21443916 | C2 | semidirect |
| 6. #21443909 | C2 | semidirect |
| 7. C61×#1387 | C2 | semidirect |
| 31. C2×D488 | Q8 | semidirect |
| 157. #1387 | D61 | semidirect |
| 183. C61 | #13369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456355 | 2 |
| #21447536 | 2 |
| C2×#16839562 | 2 |
| #21446727 | 2 |
| #21443916 | 2 |
| #21443909 | 2 |
| C61×#1387 | 2 |
| #13369 | 61 |