Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
360 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21447631 | C2 | semidirect |
| 2. #21444122 | C2 | semidirect |
| 3. #21443795 | C2 | semidirect |
| 4. #21443792 | C2 | semidirect |
| 7. #16839583 | C22 | semidirect |
| 11. #16839483 | C22 | semidirect |
| 12. C8×#92418 | C22 | semidirect |
| 59. Q16×C61 | M16 | semidirect |
| 63. D8×C61 | M16 | semidirect |
| 146. C61 | #11669 | semidirect |
| 184. Q16 | #11758194 | semidirect |
| 188. D8 | #11758194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447631 | 2 |
| #21444122 | 2 |
| #21443795 | 2 |
| #21443792 | 2 |
| C61×#2956 | 2 |
| #11669 | 61 |