Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
464 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 1. #21451044 | C2 | semidirect |
| 4. #21443699 | C2 | semidirect |
| 5. #21443686 | C2 | semidirect |
| 6. #21443666 | C2 | semidirect |
| 249. C61 | #10376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21451044 | 2 |
| #21446656 | 2 |
| C2×#16839496 | 2 |
| #21443699 | 2 |
| #21443686 | 2 |
| #21443666 | 2 |
| C61×#1519 | 2 |
| #10376 | 61 |