Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
372 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 372 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. #21447438 | C2 | semidirect |
| 3. #21445868 | C2 | semidirect |
| 4. #21443813 | C2 | semidirect |
| 5. #21443811 | C2 | semidirect |
| 6. #21443809 | C2 | semidirect |
| 7. C61×#1342 | C2 | semidirect |
| 180. #1342 | D61 | semidirect |
| 208. C61 | #11872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455483 | 2 |
| #21447438 | 2 |
| #21445868 | 2 |
| #21443813 | 2 |
| #21443811 | 2 |
| #21443809 | 2 |
| C61×#1342 | 2 |
| #11872 | 61 |