Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
498 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 498 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 |
|---|---|---|
| 2. #21446738 | C2 | semidirect |
| 3. C4×#14519708 | C2 | semidirect |
| 4. #21444314 | C2 | semidirect |
| 5. #21444313 | C2 | semidirect |
| 6. #21444106 | C2 | semidirect |
| 7. C61×#1980 | C2 | semidirect |
| 9. #16840165 | C4 | semidirect |
| 10. #16840138 | C4 | semidirect |
| 11. #16840110 | C4 | semidirect |
| 12. #16840108 | C4 | semidirect |
| 171. #92418 | #104 | semidirect |
| 197. #1980 | D61 | semidirect |
| 232. C61 | #9721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456394 | 2 |
| #21446738 | 2 |
| C4×#14519708 | 2 |
| #21444314 | 2 |
| #21444313 | 2 |
| #21444106 | 2 |
| C61×#1980 | 2 |
| #9721 | 61 |