Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
578 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 176 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 |
|---|---|---|
| 21. #16840165 | C4 | semidirect |
| 22. #16840162 | C4 | semidirect |
| 23. #16840160 | C4 | semidirect |
| 26. C61×#498 | C4 | semidirect |
| 132. #498 | #6923 | semidirect |
| 147. C61 | #22258 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462612 | 2 |
| #21462007 | 2 |
| #21461886 | 2 |
| #21461885 | 2 |
| #21461744 | 2 |
| #21461537 | 2 |
| #21456328 | 2 |
| #22258 | 61 |