Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
398 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 2. #21454924 | C2 | semidirect |
| 3. #21444527 | C2 | semidirect |
| 5. #21443731 | C2 | semidirect |
| 6. #21443681 | C2 | semidirect |
| 180. C61 | #9334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456822 | 2 |
| #21454924 | 2 |
| #21444527 | 2 |
| #21444443 | 2 |
| #21443731 | 2 |
| #21443681 | 2 |
| C61×#1469 | 2 |
| #9334 | 61 |