Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1236 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 1236 conjugacy classes of subgroups — too many to draw. Only its 231 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. #21454299 | C2 | semidirect |
| 3. #21446368 | C2 | semidirect |
| 4. #21446234 | C2 | semidirect |
| 5. #21445931 | C2 | semidirect |
| 6. #21445743 | C2 | semidirect |
| 7. C61×#1784 | C2 | semidirect |
| 189. #1784 | D61 | semidirect |
| 217. C61 | #21780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21459470 | 2 |
| #21454299 | 2 |
| #21446368 | 2 |
| #21446234 | 2 |
| #21445931 | 2 |
| #21445743 | 2 |
| C61×#1784 | 2 |
| #21780 | 61 |