Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
470 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. #21458922 | C2 | semidirect |
| 3. #21447554 | C2 | semidirect |
| 4. #21443924 | C2 | semidirect |
| 5. C61×#1812 | C2 | semidirect |
| 11. #16840020 | C4 | semidirect |
| 12. #16840015 | C4 | semidirect |
| 35. #14519717 | D4 | semidirect |
| 137. #1812 | D61 | semidirect |
| 159. C61 | #13077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458922 | 2 |
| #21455481 | 2 |
| #21447554 | 2 |
| #21443924 | 2 |
| C61×#1812 | 2 |
| #13077 | 61 |