Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
582 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 132 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. #21461556 | C2 | semidirect |
| 4. #21460662 | C2 | semidirect |
| 6. C23×#92420 | C4 | semidirect |
| 10. C2×C4⋊#92420 | C4 | semidirect |
| 11. C2×C22⋊#92420 | C4 | semidirect |
| 15. C2×C4×#92420 | C4 | semidirect |
| 17. #16840607 | C4 | semidirect |
| 18. #16840605 | C4 | semidirect |
| 112. C23×C61 | #97 | semidirect |
| 125. C2×C4×C61 | #97 | semidirect |
| 150. #92420 | #99 | semidirect |
| 209. C61 | #8160 | semidirect |
| 298. C23 | #14519832 | semidirect |
| 330. C2×C4 | #14519832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#92420 | 2 |
| #21461556 | 2 |
| #21461055 | 2 |
| #21460662 | 2 |
| #99×Dic61 | 2 |
| #8160 | 61 |