Finite Group DatabasebetaFinite Group DatabasebetaOrder 16064.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22548710 | C2 | semidirect |
| 2. #22548706 | C2 | semidirect |
| 3. #22548706 | C2 | semidirect |
| 5. #22548691 | C2 | semidirect |
| 6. Q8×Dic251 | C2 | semidirect |
| 8. #22548673 | C2 | semidirect |
| 9. #22548671 | C2 | semidirect |
| 10. C2×C4⋊Dic251 | C2 | semidirect |
| 11. C22⋊Q8×C251 | C2 | semidirect |
| 72. C251 | #552 | semidirect |
| 79. C22⋊Q8 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22548710 | 2 |
| #22548706 | 2 |
| #22548699 | 2 |
| #22548691 | 2 |
| Q8×Dic251 | 2 |
| C4×C22⋊D251 | 2 |
| #22548673 | 2 |
| #22548671 | 2 |
| C2×C4⋊Dic251 | 2 |
| C22⋊Q8×C251 | 2 |
| #552 | 251 |