Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
314 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×D61⋊C16 | C4 | semidirect |
| 9. #16840636 | C4 | semidirect |
| 13. #16839525 | C4 | semidirect |
| 14. C61×#340 | C4 | semidirect |
| 150. #340 | #6923 | semidirect |
| 151. C61 | #7230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊(C22⋊C16) | 2 |
| #21461696 | 2 |
| #21445847 | 2 |
| #7230 | 61 |