Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
344 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21447488 | C2 | semidirect |
| 3. #21443995 | C2 | semidirect |
| 4. #21443977 | C2 | semidirect |
| 5. C61×#2134 | C2 | semidirect |
| 6. #16840367 | C4 | semidirect |
| 8. #16840138 | C4 | semidirect |
| 9. #16840126 | C4 | semidirect |
| 15. #16839823 | C4 | semidirect |
| 27. #14519774 | C2×C4 | semidirect |
| 28. #14519769 | C2×C4 | semidirect |
| 42. #14519688 | C2×C4 | semidirect |
| 43. C4×#92418 | C2×C4 | semidirect |
| 153. #2134 | D61 | semidirect |
| 181. C61 | #13605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456869 | 2 |
| #21447488 | 2 |
| #21443995 | 2 |
| #21443977 | 2 |
| C61×#2134 | 2 |
| #13605 | 61 |