Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
684 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 684 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 |
|---|---|---|
| 1. #21456822 | C2 | semidirect |
| 2. #21456193 | C2 | semidirect |
| 3. #21444533 | C2 | semidirect |
| 4. #21444417 | C2 | semidirect |
| 5. #21444330 | C2 | semidirect |
| 6. #21443712 | C2 | semidirect |
| 34. #14519777 | D4 | semidirect |
| 35. #14519777 | D4 | semidirect |
| 43. C4⋊#92418 | D4 | semidirect |
| 52. #14519688 | D4 | semidirect |
| 231. C61 | #10096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456822 | 2 |
| #21456193 | 2 |
| #21444533 | 2 |
| #21444417 | 2 |
| #21444330 | 2 |
| #21443712 | 2 |
| C61×#2657 | 2 |
| #10096 | 61 |