Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
332 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×C4×#11758185 | C2 | semidirect |
| 5. #21443914 | C2 | semidirect |
| 6. #21443912 | C2 | semidirect |
| 7. C61×#1945 | C2 | semidirect |
| 15. #16839565 | C4 | semidirect |
| 16. #16839562 | C4 | semidirect |
| 137. #1945 | D61 | semidirect |
| 160. C61 | #13151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839568 | 2 |
| #21447524 | 2 |
| C2×C4×#11758185 | 2 |
| #21446707 | 2 |
| #21443914 | 2 |
| #21443912 | 2 |
| C61×#1945 | 2 |
| #13151 | 61 |