Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
380 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 9. #16840158 | C4 | semidirect |
| 10. #16840141 | C4 | semidirect |
| 11. #16840114 | C4 | semidirect |
| 12. #16840112 | C4 | semidirect |
| 174. C61 | #9416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456560 | 2 |
| #21454924 | 2 |
| #21444371 | 2 |
| #21444370 | 2 |
| #21443690 | 2 |
| #21443685 | 2 |
| C61×#1537 | 2 |
| #9416 | 61 |