Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
558 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21454536 | C2 | semidirect |
| 3. #21446644 | C2 | semidirect |
| 4. #21444380 | C2 | semidirect |
| 5. #21443679 | C2 | semidirect |
| 6. #21443649 | C2 | semidirect |
| 7. C61×#1545 | C2 | semidirect |
| 10. #16840138 | C4 | semidirect |
| 11. #16840108 | C4 | semidirect |
| 116. C2×#92418 | D8 | semidirect |
| 192. #1545 | D61 | semidirect |
| 222. C61 | #9293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456737 | 2 |
| #21454536 | 2 |
| #21446644 | 2 |
| #21444380 | 2 |
| #21443679 | 2 |
| #21443649 | 2 |
| C61×#1545 | 2 |
| #9293 | 61 |