Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
372 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 4. C23×#92418 | C4 | semidirect |
| 7. C2×C22⋊#92418 | C4 | semidirect |
| 14. C61×#343 | C4 | semidirect |
| 174. #343 | Dic61 | semidirect |
| 177. C61 | #7236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21446112 | 2 |
| #21445807 | 2 |
| C61×#1800 | 2 |
| #7236 | 61 |