Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
3550 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 3550 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. #21454071 | C2 | direct (N × H) |
| 2. C2×#16839675 | C2 | semidirect |
| 3. C2×#16839674 | C2 | semidirect |
| 4. C2×#16839673 | C2 | semidirect |
| 6. C2×C61×#393 | C2 | semidirect |
| 8. C23×Dic122 | C22 | semidirect |
| 12. #16839675 | C22 | semidirect |
| 13. #16839674 | C22 | semidirect |
| 14. #16839673 | C22 | semidirect |
| 16. C2×#14519684 | C22 | semidirect |
| 17. C2×#14519684 | C22 | semidirect |
| 18. C23×Q8×C61 | C22 | semidirect |
| 20. C61×#393 | C22 | semidirect |
| 21. C2×#95×C61 | C22 | semidirect |
| 24. C24×D61 | Q8 | semidirect |
| 29. C22×Dic122 | C23 | semidirect |
| 37. #14519684 | C23 | semidirect |
| 38. #14519684 | C23 | semidirect |
| 41. C22×Q8×C61 | C23 | semidirect |
| 46. #95×C61 | C23 | semidirect |
| 60. C23×D61 | C2×Q8 | semidirect |
| 136. C2×#393 | D61 | semidirect |
| 139. C2×C61 | #2840 | semidirect |
| 146. C23×Q8 | C2×D61 | semidirect |
| 154. #393 | C2×D61 | semidirect |
| 158. C2×#95 | C2×D61 | semidirect |
| 159. C61 | C2×#2840 | semidirect |
| 170. C22×Q8 | C22×D61 | semidirect |
| 184. #95 | C22×D61 | semidirect |
| 271. C2 | #21454071 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454071 | 2 |
| C2×#16839675 | 2 |
| C2×#16839674 | 2 |
| C2×#16839673 | 2 |
| C2×#16839617 | 2 |
| C2×C61×#393 | 2 |
| C2×#2840 | 61 |