Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
348 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 73 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. #21445959 | C2 | semidirect |
| 3. #21444550 | C2 | semidirect |
| 5. #21444435 | C2 | semidirect |
| 7. C61×#1307 | C2 | semidirect |
| 155. #1307 | D61 | semidirect |
| 180. C61 | #10527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457207 | 2 |
| #21445959 | 2 |
| #21444550 | 2 |
| #21444542 | 2 |
| #21444435 | 2 |
| #21444431 | 2 |
| C61×#1307 | 2 |
| #10527 | 61 |