Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 2. #21447592 | C2 | semidirect |
| 5. #21443916 | C2 | semidirect |
| 6. #21443914 | C2 | semidirect |
| 7. C61×#2155 | C2 | semidirect |
| 11. C2×#14519716 | C4 | semidirect |
| 13. C2×C16×D61 | C4 | semidirect |
| 137. #2155 | D61 | semidirect |
| 164. C61 | #12832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840180 | 2 |
| #21447592 | 2 |
| #21445866 | 2 |
| #21445862 | 2 |
| #21443916 | 2 |
| #21443914 | 2 |
| C61×#2155 | 2 |
| #12832 | 61 |