Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
478 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16840165 | C4 | semidirect |
| 10. #16840141 | C4 | semidirect |
| 11. #16840114 | C4 | semidirect |
| 12. #16840112 | C4 | semidirect |
| 86. C42×C61 | Q16 | semidirect |
| 181. C61 | #9845 | semidirect |
| 257. C42 | #11758202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456401 | 2 |
| #21446796 | 2 |
| C42×#92418 | 2 |
| #21444577 | 2 |
| #21444274 | 2 |
| #21444273 | 2 |
| C61×#1994 | 2 |
| #9845 | 61 |