Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
518 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21454859 | C2 | semidirect |
| 3. #21445830 | C2 | semidirect |
| 4. #21444379 | C2 | semidirect |
| 5. #21443716 | C2 | semidirect |
| 6. #21443678 | C2 | semidirect |
| 7. C61×#1480 | C2 | semidirect |
| 11. #16839964 | C4 | semidirect |
| 12. #16839954 | C4 | semidirect |
| 192. #1480 | D61 | semidirect |
| 221. C61 | #9309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455279 | 2 |
| #21454859 | 2 |
| #21445830 | 2 |
| #21444379 | 2 |
| #21443716 | 2 |
| #21443678 | 2 |
| C61×#1480 | 2 |
| #9309 | 61 |