Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
458 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. C2×#16839577 | C2 | semidirect |
| 4. C2×#16839567 | C2 | semidirect |
| 6. #21443929 | C2 | semidirect |
| 7. C61×#1381 | C2 | semidirect |
| 17. #16840038 | C4 | semidirect |
| 171. #1381 | D61 | semidirect |
| 198. C61 | #13072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840178 | 2 |
| C2×#16840038 | 2 |
| C2×#16839577 | 2 |
| C2×#16839567 | 2 |
| #21445880 | 2 |
| #21443929 | 2 |
| C61×#1381 | 2 |
| #13072 | 61 |