Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
3294 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 627 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 |
|---|---|---|
| 1. #21454084 | C2 | direct (N × H) |
| 2. C2×#16839698 | C2 | semidirect |
| 3. C2×#16839686 | C2 | semidirect |
| 4. C2×#16839684 | C2 | semidirect |
| 6. C2×C61×#399 | C2 | semidirect |
| 8. C22×C4⋊Dic61 | C22 | semidirect |
| 9. C22×#11758196 | C22 | semidirect |
| 13. #16839698 | C22 | semidirect |
| 14. #16839686 | C22 | semidirect |
| 15. #16839684 | C22 | semidirect |
| 17. C2×#14519684 | C22 | semidirect |
| 18. C22×C4⋊C4×C61 | C22 | semidirect |
| 20. C61×#399 | C22 | semidirect |
| 21. C2×#95×C61 | C22 | semidirect |
| 29. C2×C4⋊Dic61 | C23 | semidirect |
| 31. C2×#11758196 | C23 | semidirect |
| 38. #14519684 | C23 | semidirect |
| 43. C2×C4⋊C4×C61 | C23 | semidirect |
| 46. #95×C61 | C23 | semidirect |
| 130. C2×#399 | D61 | semidirect |
| 135. C2×C61 | #2842 | semidirect |
| 143. C22×C4⋊C4 | C2×D61 | semidirect |
| 149. #399 | C2×D61 | semidirect |
| 154. C2×#95 | C2×D61 | semidirect |
| 155. C61 | C2×#2842 | semidirect |
| 170. C2×C4⋊C4 | C22×D61 | semidirect |
| 180. #95 | C22×D61 | semidirect |
| 263. C2 | #21454084 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454084 | 2 |
| C2×#16839698 | 2 |
| C2×#16839686 | 2 |
| C2×#16839684 | 2 |
| C2×#16839617 | 2 |
| C2×C61×#399 | 2 |
| C2×#2842 | 61 |