Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
392 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 87 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. #21447574 | C2 | semidirect |
| 3. #21447569 | C2 | semidirect |
| 4. #21446708 | C2 | semidirect |
| 5. #21446705 | C2 | semidirect |
| 6. #21443922 | C2 | semidirect |
| 7. C61×#2148 | C2 | semidirect |
| 179. #2148 | D61 | semidirect |
| 210. C61 | #13444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458953 | 2 |
| #21447574 | 2 |
| #21447569 | 2 |
| #21446708 | 2 |
| #21446705 | 2 |
| #21443922 | 2 |
| C61×#2148 | 2 |
| #13444 | 61 |