Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
438 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 3. #21462034 | C2 | semidirect |
| 4. #21461635 | C2 | semidirect |
| 5. #21460894 | C2 | semidirect |
| 6. #21460883 | C2 | semidirect |
| 10. #16840809 | C4 | semidirect |
| 11. #16840809 | C4 | semidirect |
| 12. #16840808 | C4 | semidirect |
| 13. #16840808 | C4 | semidirect |
| 21. #16840675 | C4 | semidirect |
| 22. #16840674 | C4 | semidirect |
| 29. #16839573 | C4 | semidirect |
| 30. #16839572 | C4 | semidirect |
| 31. #16839571 | C4 | semidirect |
| 32. C61×#360 | C4 | semidirect |
| 118. Q16×C61 | C42 | semidirect |
| 120. D8×C61 | C42 | semidirect |
| 130. Dic244 | C42 | semidirect |
| 131. D488 | C42 | semidirect |
| 236. #360 | #6923 | semidirect |
| 242. C61 | #12650 | semidirect |
| 308. Q16 | C4×#6923 | semidirect |
| 315. D8 | C4×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#444 | 2 |
| #21462127 | 2 |
| #21462034 | 2 |
| #21461635 | 2 |
| #21460894 | 2 |
| #21460883 | 2 |
| #360×D61 | 2 |
| #12650 | 61 |