Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
376 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 72 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. #21462056 | C2 | semidirect |
| 2. #21461701 | C2 | semidirect |
| 3. #21460791 | C2 | semidirect |
| 4. #21460789 | C2 | semidirect |
| 14. #16840017 | C4 | semidirect |
| 16. #16840012 | C4 | semidirect |
| 20. C2×#14519709 | C4 | semidirect |
| 22. C2×#135×C61 | C4 | semidirect |
| 177. C2×#135 | #6923 | semidirect |
| 194. C61 | #11867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462056 | 2 |
| #21461701 | 2 |
| #21460791 | 2 |
| #21460789 | 2 |
| #21455477 | 2 |
| #11867 | 61 |