Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
642 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 194 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. #21461919 | C2 | semidirect |
| 3. #21461877 | C2 | semidirect |
| 5. #21461751 | C2 | semidirect |
| 6. #21461746 | C2 | semidirect |
| 66. C42×C61 | M16 | semidirect |
| 143. C61 | #23378 | semidirect |
| 194. C42 | #11758213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461919 | 2 |
| #21461894 | 2 |
| #21461877 | 2 |
| #21461765 | 2 |
| #21461751 | 2 |
| #21461746 | 2 |
| #21448367 | 2 |
| #23378 | 61 |