Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
422 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 104 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. #16840802 | C4 | semidirect |
| 17. #16840681 | C4 | semidirect |
| 23. #16839567 | C4 | semidirect |
| 24. #16839566 | C4 | semidirect |
| 25. #16839565 | C4 | semidirect |
| 26. C61×#358 | C4 | semidirect |
| 181. #358 | #6923 | semidirect |
| 184. C61 | #12648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840802 | 2 |
| C2×#16840681 | 2 |
| C2×#16840653 | 2 |
| #21461626 | 2 |
| #21460890 | 2 |
| #21460884 | 2 |
| #21447537 | 2 |
| #12648 | 61 |