Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
414 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 11. #16840626 | C4 | semidirect |
| 12. #16840623 | C4 | semidirect |
| 17. #16839514 | C4 | semidirect |
| 18. #16839513 | C4 | semidirect |
| 19. C61×#334 | C4 | semidirect |
| 31. C8×#6923 | C8 | semidirect |
| 124. #334 | #6923 | semidirect |
| 127. C61 | #8266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C8×#6923 | 2 |
| #21461367 | 2 |
| #21461025 | 2 |
| #21460646 | 2 |
| #21444564 | 2 |
| #8266 | 61 |