Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
554 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 125 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. #21446647 | C2 | semidirect |
| 3. C42×#92418 | C2 | semidirect |
| 4. #21444577 | C2 | semidirect |
| 5. #21444270 | C2 | semidirect |
| 6. #21444269 | C2 | semidirect |
| 7. C61×#1962 | C2 | semidirect |
| 9. #16840165 | C4 | semidirect |
| 10. #16840138 | C4 | semidirect |
| 11. #16840110 | C4 | semidirect |
| 12. #16840108 | C4 | semidirect |
| 96. C42×C61 | D8 | semidirect |
| 149. #92418 | #104 | semidirect |
| 173. #1962 | D61 | semidirect |
| 203. C61 | #9844 | semidirect |
| 285. C42 | #11758199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456394 | 2 |
| #21446647 | 2 |
| C42×#92418 | 2 |
| #21444577 | 2 |
| #21444270 | 2 |
| #21444269 | 2 |
| C61×#1962 | 2 |
| #9844 | 61 |