Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
474 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 109 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×#16839870 | C2 | semidirect |
| 3. C2×#16839577 | C2 | semidirect |
| 5. #21443919 | C2 | semidirect |
| 6. #21443899 | C2 | semidirect |
| 12. C2×#14519723 | C4 | semidirect |
| 13. C2×#14519721 | C4 | semidirect |
| 196. C61 | #13038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840202 | 2 |
| C2×#16839870 | 2 |
| C2×#16839577 | 2 |
| C2×#16839572 | 2 |
| #21443919 | 2 |
| #21443899 | 2 |
| C61×#1975 | 2 |
| #13038 | 61 |