Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
766 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21446617 | C2 | semidirect |
| 3. #21444519 | C2 | semidirect |
| 4. #21444515 | C2 | semidirect |
| 5. #21444429 | C2 | semidirect |
| 6. #21444159 | C2 | semidirect |
| 7. C61×#1531 | C2 | semidirect |
| 221. #1531 | D61 | semidirect |
| 255. C61 | #8458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21459673 | 2 |
| #21446617 | 2 |
| #21444519 | 2 |
| #21444515 | 2 |
| #21444429 | 2 |
| #21444159 | 2 |
| C61×#1531 | 2 |
| #8458 | 61 |