Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
492 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #21446664 | C2 | semidirect |
| 5. #21444240 | C2 | semidirect |
| 6. #21443709 | C2 | semidirect |
| 7. C61×#3165 | C2 | semidirect |
| 177. #3165 | D61 | semidirect |
| 210. C61 | #10116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457202 | 2 |
| #21456947 | 2 |
| #21446664 | 2 |
| #21444410 | 2 |
| #21444240 | 2 |
| #21443709 | 2 |
| C61×#3165 | 2 |
| #10116 | 61 |