Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
432 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×#16839582 | C2 | semidirect |
| 3. C2×#16839576 | C2 | semidirect |
| 4. #21446708 | C2 | semidirect |
| 5. #21446683 | C2 | semidirect |
| 6. #21443927 | C2 | semidirect |
| 7. C61×#2139 | C2 | semidirect |
| 173. #2139 | D61 | semidirect |
| 203. C61 | #13445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840197 | 2 |
| C2×#16839582 | 2 |
| C2×#16839576 | 2 |
| #21446708 | 2 |
| #21446683 | 2 |
| #21443927 | 2 |
| C61×#2139 | 2 |
| #13445 | 61 |