Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
536 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 135 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. #21456469 | C2 | semidirect |
| 2. #21448033 | C2 | semidirect |
| 3. #21447995 | C2 | semidirect |
| 4. #21447895 | C2 | semidirect |
| 5. #21447765 | C2 | semidirect |
| 6. #21447717 | C2 | semidirect |
| 7. #21447635 | C2 | semidirect |
| 8. C61×#2955 | C2 | semidirect |
| 11. #16840164 | C22 | semidirect |
| 12. #16840139 | C22 | semidirect |
| 16. #16839875 | C22 | semidirect |
| 18. #16839586 | C22 | semidirect |
| 19. #16839583 | C22 | semidirect |
| 20. #16839574 | C22 | semidirect |
| 23. #16839540 | C22 | semidirect |
| 163. #2955 | D61 | semidirect |
| 199. C61 | #33692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456469 | 2 |
| #21448033 | 2 |
| #21447995 | 2 |
| #21447895 | 2 |
| #21447765 | 2 |
| #21447717 | 2 |
| #21447635 | 2 |
| C61×#2955 | 2 |
| #33692 | 61 |