Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21444422 | C2 | semidirect |
| 5. #21444176 | C2 | semidirect |
| 6. #21443669 | C2 | semidirect |
| 7. C61×#1290 | C2 | semidirect |
| 202. #1290 | D61 | semidirect |
| 236. C61 | #9245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840063 | 2 |
| #21454856 | 2 |
| #21444422 | 2 |
| #21444261 | 2 |
| #21444176 | 2 |
| #21443669 | 2 |
| C61×#1290 | 2 |
| #9245 | 61 |