Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
598 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21451760 | C2 | semidirect |
| 3. #21444545 | C2 | semidirect |
| 4. #21444416 | C2 | semidirect |
| 5. #21444327 | C2 | semidirect |
| 6. #21443713 | C2 | semidirect |
| 7. C61×#3152 | C2 | semidirect |
| 186. #3152 | D61 | semidirect |
| 221. C61 | #10090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456802 | 2 |
| #21451760 | 2 |
| #21444545 | 2 |
| #21444416 | 2 |
| #21444327 | 2 |
| #21443713 | 2 |
| C61×#3152 | 2 |
| #10090 | 61 |