Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
466 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 120 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. C4×#14519852 | C2 | semidirect |
| 3. C4×#14519845 | C2 | semidirect |
| 4. #21460890 | C2 | semidirect |
| 9. #16840678 | C4 | direct (N × H) |
| 15. C4×Dic244 | C4 | semidirect |
| 16. #16839856 | C4 | semidirect |
| 19. D8×Dic61 | C4 | semidirect |
| 23. C4×D8×C61 | C4 | semidirect |
| 27. #14519852 | C2×C4 | semidirect |
| 30. #14519845 | C2×C4 | semidirect |
| 77. D8×C61 | C42 | semidirect |
| 98. Dic244 | C42 | semidirect |
| 145. C4×C61 | #360 | semidirect |
| 171. C4×D8 | #6923 | semidirect |
| 181. C61 | C4×#360 | semidirect |
| 235. D8 | C4×#6923 | semidirect |
| 307. C4 | #16840678 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840678 | 2 |
| C4×#14519852 | 2 |
| C4×#14519845 | 2 |
| #21460890 | 2 |
| C4×#14519796 | 2 |
| C4×#360 | 61 |