Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
516 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 516 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. #21446796 | C2 | semidirect |
| 3. C42×#92418 | C2 | semidirect |
| 4. #21444574 | C2 | semidirect |
| 5. #21444273 | C2 | semidirect |
| 9. #16840158 | C4 | semidirect |
| 10. #16840134 | C4 | semidirect |
| 11. #16840114 | C4 | semidirect |
| 12. #16840108 | C4 | semidirect |
| 89. C42×C61 | SD16 | semidirect |
| 141. #92418 | #104 | semidirect |
| 192. C61 | #9843 | semidirect |
| 271. C42 | #11758200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456374 | 2 |
| #21446796 | 2 |
| C42×#92418 | 2 |
| #21444574 | 2 |
| #21444273 | 2 |
| #21444270 | 2 |
| C61×#1962 | 2 |
| #9843 | 61 |