Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
748 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×#16840200 | C2 | semidirect |
| 2. C22×#14519718 | C2 | semidirect |
| 3. #21456300 | C2 | semidirect |
| 4. #21454670 | C2 | semidirect |
| 5. #21447873 | C2 | semidirect |
| 6. #21447853 | C2 | semidirect |
| 7. #21447579 | C2 | semidirect |
| 8. #21447524 | C2 | semidirect |
| 9. C61×#2140 | C2 | semidirect |
| 16. C2×#14519722 | C22 | semidirect |
| 17. C2×D976 | C22 | semidirect |
| 22. #16840145 | C22 | semidirect |
| 23. #16840137 | C22 | semidirect |
| 25. #16839844 | C22 | semidirect |
| 28. #16839580 | C22 | semidirect |
| 29. #16839565 | C22 | semidirect |
| 30. #16839562 | C22 | semidirect |
| 34. C61×#357 | C22 | semidirect |
| 45. C2×D488 | D4 | semidirect |
| 183. #2140 | D61 | semidirect |
| 215. #357 | C2×D61 | semidirect |
| 216. C61 | #33585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840200 | 2 |
| C22×#14519718 | 2 |
| #21456300 | 2 |
| #21454670 | 2 |
| #21447873 | 2 |
| #21447853 | 2 |
| #21447579 | 2 |
| #21447524 | 2 |
| C61×#2140 | 2 |
| #33585 | 61 |