Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
384 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. C4×#14519710 | C2 | semidirect |
| 3. #21444580 | C2 | semidirect |
| 6. #21443676 | C2 | semidirect |
| 7. C61×#1285 | C2 | semidirect |
| 9. #16839889 | C4 | semidirect |
| 10. #16839886 | C4 | semidirect |
| 11. #16839839 | C4 | semidirect |
| 13. #16839827 | C4 | semidirect |
| 179. #1285 | D61 | semidirect |
| 209. C61 | #8697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454788 | 2 |
| C4×#14519710 | 2 |
| #21444580 | 2 |
| #21444345 | 2 |
| #21444342 | 2 |
| #21443676 | 2 |
| C61×#1285 | 2 |
| #8697 | 61 |