Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21444591 | C2 | semidirect |
| 4. #21444474 | C2 | semidirect |
| 5. #21444382 | C2 | semidirect |
| 7. C61×#1286 | C2 | semidirect |
| 173. #1286 | D61 | semidirect |
| 199. C61 | #10468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455618 | 2 |
| #21445826 | 2 |
| #21444591 | 2 |
| #21444474 | 2 |
| #21444382 | 2 |
| #21444139 | 2 |
| C61×#1286 | 2 |
| #10468 | 61 |