Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
336 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 3. #21443989 | C2 | semidirect |
| 4. #21443983 | C2 | semidirect |
| 6. #16840374 | C4 | semidirect |
| 7. #16840157 | C4 | semidirect |
| 10. #16840116 | C4 | semidirect |
| 15. #16839823 | C4 | semidirect |
| 27. #14519777 | C2×C4 | semidirect |
| 29. #14519769 | C2×C4 | semidirect |
| 42. #14519688 | C2×C4 | semidirect |
| 43. C4×#92418 | C2×C4 | semidirect |
| 176. C61 | #13610 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456891 | 2 |
| #21447488 | 2 |
| #21443989 | 2 |
| #21443983 | 2 |
| C61×#2128 | 2 |
| #13610 | 61 |