Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
460 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 111 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. C4×#14519710 | C2 | semidirect |
| 4. #21444318 | C2 | semidirect |
| 6. #21444106 | C2 | semidirect |
| 7. C61×#1986 | C2 | semidirect |
| 9. #16840158 | C4 | semidirect |
| 10. #16840136 | C4 | semidirect |
| 11. #16840112 | C4 | semidirect |
| 12. #16840110 | C4 | semidirect |
| 163. #92418 | #104 | semidirect |
| 186. #1986 | D61 | semidirect |
| 221. C61 | #9722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456379 | 2 |
| #21446738 | 2 |
| C4×#14519710 | 2 |
| #21444318 | 2 |
| #21444313 | 2 |
| #21444106 | 2 |
| C61×#1986 | 2 |
| #9722 | 61 |