Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
816 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 123 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. #21446789 | C2 | semidirect |
| 3. #21446635 | C2 | semidirect |
| 4. C2×#16839501 | C2 | semidirect |
| 5. C2×C61×#330 | C2 | semidirect |
| 8. #16840510 | C4 | semidirect |
| 152. C2×#330 | D61 | semidirect |
| 176. C61 | #8508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840510 | 2 |
| #21446789 | 2 |
| #21446635 | 2 |
| C2×#16839501 | 2 |
| C2×C61×#330 | 2 |
| #8508 | 61 |