Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1250 conjugacy classes of subgroups; only the 344 normal subgroups are shown.
This group has 1250 conjugacy classes of subgroups — too many to draw. Only its 344 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 |
|---|---|---|
| 2. #21461556 | C2 | semidirect |
| 3. C22⋊C4×#92420 | C2 | semidirect |
| 4. #21461549 | C2 | semidirect |
| 7. C2×C22⋊#92420 | C4 | semidirect |
| 11. C2×#14519832 | C22 | semidirect |
| 12. C2×C4×#92420 | C22 | semidirect |
| 13. #16840628 | C22 | semidirect |
| 147. C61 | #20528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#92420 | 2 |
| #21461556 | 2 |
| C22⋊C4×#92420 | 2 |
| #21461549 | 2 |
| #21448197 | 2 |
| #20528 | 61 |