Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
326 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 3. #21443989 | C2 | semidirect |
| 5. C2×#14519769 | C4 | semidirect |
| 6. #16840130 | C4 | semidirect |
| 13. C4×#11758194 | C4 | semidirect |
| 152. C61 | #13596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456219 | 2 |
| #21447484 | 2 |
| #21443989 | 2 |
| C61×#2126 | 2 |
| #13596 | 61 |