Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
530 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21448632 | C2 | semidirect |
| 3. #21444416 | C2 | semidirect |
| 4. #21444366 | C2 | semidirect |
| 5. #21443684 | C2 | semidirect |
| 6. #21443675 | C2 | semidirect |
| 7. C61×#1980 | C2 | semidirect |
| 9. #16840149 | C4 | semidirect |
| 10. #16840124 | C4 | semidirect |
| 54. #14519688 | C2×C4 | semidirect |
| 63. C4⋊Q8×C61 | C2×C4 | semidirect |
| 64. #127×C61 | C2×C4 | semidirect |
| 217. #1980 | D61 | semidirect |
| 252. C61 | #9381 | semidirect |
| 260. C4⋊Q8 | C4×D61 | semidirect |
| 261. #127 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456802 | 2 |
| #21448632 | 2 |
| #21444416 | 2 |
| #21444366 | 2 |
| #21443684 | 2 |
| #21443675 | 2 |
| C61×#1980 | 2 |
| #9381 | 61 |