Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
5942 conjugacy classes of subgroups; only the 387 normal subgroups are shown.
This group has 5942 conjugacy classes of subgroups — too many to draw. Only its 387 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×#16839913 | C2 | semidirect |
| 2. #21454106 | C2 | semidirect |
| 3. #21445750 | C2 | semidirect |
| 4. #21445729 | C2 | semidirect |
| 6. C22×#11758200 | C22 | semidirect |
| 7. C2×#14519756 | C22 | semidirect |
| 9. C2×#14519698 | C22 | semidirect |
| 10. C2×C22⋊#92418 | C22 | semidirect |
| 12. #16839622 | C22 | semidirect |
| 19. C22×Dic122 | C23 | semidirect |
| 21. C22×#92418 | C23 | semidirect |
| 23. C2×C4⋊Dic61 | C23 | semidirect |
| 57. C24×C61 | SD16 | semidirect |
| 123. C22×C61 | #450 | semidirect |
| 154. C61 | #32881 | semidirect |
| 193. C24 | #11758200 | semidirect |
| 258. C22 | #16839913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839913 | 2 |
| #21454106 | 2 |
| #21445750 | 2 |
| #21445729 | 2 |
| C24×D4×C61 | 2 |
| #32881 | 61 |