Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
332 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 332 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 |
|---|---|---|
| 4. #21446567 | C2 | semidirect |
| 5. #21443915 | C2 | semidirect |
| 6. #21443913 | C2 | semidirect |
| 7. C2×C4×C16×C61 | C2 | semidirect |
| 16. #16839567 | C4 | semidirect |
| 17. #16839564 | C4 | semidirect |
| 135. C2×C4×C16 | 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×#16839570 | 2 |
| #21447527 | 2 |
| #21446707 | 2 |
| #21446567 | 2 |
| #21443915 | 2 |
| #21443913 | 2 |
| C2×C4×C16×C61 | 2 |
| #13151 | 61 |