Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
388 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 20. #16839577 | C4 | semidirect |
| 176. C61 | #12941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454686 | 2 |
| #21447608 | 2 |
| C2×#16839577 | 2 |
| C2×#16839567 | 2 |
| #21446605 | 2 |
| #21443907 | 2 |
| C61×#1382 | 2 |
| #12941 | 61 |