Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
384 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×#16839586 | C2 | semidirect |
| 5. #21446600 | C2 | semidirect |
| 6. #21443904 | C2 | semidirect |
| 7. C61×#1388 | C2 | semidirect |
| 18. #16839577 | C4 | semidirect |
| 19. #16839574 | C4 | semidirect |
| 145. #1388 | D61 | semidirect |
| 169. C61 | #12952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454735 | 2 |
| C2×#16839586 | 2 |
| #21447566 | 2 |
| C2×#16839573 | 2 |
| #21446600 | 2 |
| #21443904 | 2 |
| C61×#1388 | 2 |
| #12952 | 61 |