Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
318 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 57 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. #21448021 | C2 | semidirect |
| 3. #21447260 | C2 | semidirect |
| 4. #21443838 | C2 | semidirect |
| 5. #21443834 | C2 | semidirect |
| 6. #21443744 | C2 | semidirect |
| 7. C61×#2232 | C2 | semidirect |
| 153. #2232 | D61 | semidirect |
| 183. C61 | #12287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456715 | 2 |
| #21448021 | 2 |
| #21447260 | 2 |
| #21443838 | 2 |
| #21443834 | 2 |
| #21443744 | 2 |
| C61×#2232 | 2 |
| #12287 | 61 |