Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
394 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 16. #16840165 | C4 | semidirect |
| 19. #16840160 | C4 | semidirect |
| 23. C61×#498 | C4 | semidirect |
| 136. #498 | #6923 | semidirect |
| 149. C61 | #9755 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461756 | 2 |
| #21461253 | 2 |
| #21461251 | 2 |
| #21461023 | 2 |
| #21456328 | 2 |
| #9755 | 61 |