Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21448567 | C2 | semidirect |
| 3. #21444501 | C2 | semidirect |
| 5. #21443679 | C2 | semidirect |
| 6. #21443648 | C2 | semidirect |
| 9. #16840134 | C4 | semidirect |
| 10. #16840114 | C4 | semidirect |
| 97. C42×C61 | SD16 | semidirect |
| 209. C61 | #9301 | semidirect |
| 291. C42 | #11758200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456741 | 2 |
| #21448567 | 2 |
| #21444501 | 2 |
| #21444379 | 2 |
| #21443679 | 2 |
| #21443648 | 2 |
| C61×#1963 | 2 |
| #9301 | 61 |