Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
498 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21457017 | C2 | semidirect |
| 3. #21444453 | C2 | semidirect |
| 4. #21444292 | C2 | semidirect |
| 5. #21444160 | C2 | semidirect |
| 6. #21443680 | C2 | semidirect |
| 7. C61×#3110 | C2 | semidirect |
| 191. #3110 | D61 | semidirect |
| 228. C61 | #10042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457017 | 2 |
| #21455819 | 2 |
| #21444453 | 2 |
| #21444292 | 2 |
| #21444160 | 2 |
| #21443680 | 2 |
| C61×#3110 | 2 |
| #10042 | 61 |