Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
558 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 1. #21462548 | C2 | semidirect |
| 2. #21461951 | C2 | semidirect |
| 3. #21461327 | C2 | semidirect |
| 4. #21461248 | C2 | semidirect |
| 5. #21460673 | C2 | semidirect |
| 6. #21460644 | C2 | semidirect |
| 22. #16840138 | C4 | semidirect |
| 23. #16840109 | C4 | semidirect |
| 24. #16840108 | C4 | semidirect |
| 28. C61×#493 | C4 | semidirect |
| 117. D61⋊C8 | D8 | semidirect |
| 228. #493 | #6923 | semidirect |
| 245. C61 | #9293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462548 | 2 |
| #21461951 | 2 |
| #21461327 | 2 |
| #21461248 | 2 |
| #21460673 | 2 |
| #21460644 | 2 |
| #21456733 | 2 |
| #9293 | 61 |