Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
318 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 318 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 |
|---|---|---|
| 14. #16840689 | C4 | semidirect |
| 15. #16840688 | C4 | semidirect |
| 16. #16840653 | C4 | semidirect |
| 17. #16840652 | C4 | semidirect |
| 23. #16839586 | C4 | semidirect |
| 24. #16839585 | C4 | semidirect |
| 25. #16839584 | C4 | semidirect |
| 26. C61×#365 | C4 | semidirect |
| 92. C16×C61 | C42 | semidirect |
| 93. #11758185 | C42 | semidirect |
| 165. #365 | #6923 | semidirect |
| 170. C61 | #12677 | semidirect |
| 237. C16 | C4×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462171 | 2 |
| #21462034 | 2 |
| #21461635 | 2 |
| #21461628 | 2 |
| #21460895 | 2 |
| #21460892 | 2 |
| #365×D61 | 2 |
| #12677 | 61 |