Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
358 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 10. #16840648 | C4 | semidirect |
| 11. C4×#11758187 | C4 | semidirect |
| 14. #16839538 | C4 | semidirect |
| 15. #16839537 | C4 | semidirect |
| 16. C61×#346 | C4 | semidirect |
| 96. #346 | #6923 | semidirect |
| 99. C61 | #12592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D61⋊C16 | 2 |
| #21461475 | 2 |
| (C2×#6923)⋊C16 | 2 |
| #346×D61 | 2 |
| #12592 | 61 |