Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
532 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 15. #16840619 | C4 | semidirect |
| 18. #16839504 | C4 | semidirect |
| 19. #16839503 | C4 | semidirect |
| 20. C61×#330 | C4 | semidirect |
| 113. #6923 | #330 | direct (N × H) |
| 144. #330 | #6923 | direct (N × H) |
| 145. C61 | C4×#330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #125×#6923 | 2 |
| #97×#6923 | 2 |
| D61⋊#330 | 2 |
| #21460696 | 2 |
| #330×D61 | 2 |
| C4×#330 | 61 |