Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
462 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 462 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. #21454737 | C2 | semidirect |
| 3. C2×#16839569 | C2 | semidirect |
| 4. #21447524 | C2 | semidirect |
| 5. #21443935 | C2 | semidirect |
| 6. #21443908 | C2 | semidirect |
| 7. C61×#1976 | C2 | semidirect |
| 10. #16840203 | C4 | semidirect |
| 12. #16840198 | C4 | semidirect |
| 179. #1976 | D61 | semidirect |
| 209. C61 | #13021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458953 | 2 |
| #21454737 | 2 |
| C2×#16839569 | 2 |
| #21447524 | 2 |
| #21443935 | 2 |
| #21443908 | 2 |
| C61×#1976 | 2 |
| #13021 | 61 |