Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22551591 | C2 | semidirect |
| 2. #22551587 | C2 | semidirect |
| 3. #22551585 | C2 | semidirect |
| 5. #22551568 | C2 | semidirect |
| 6. Q8×Dic257 | C2 | semidirect |
| 7. #22551557 | C2 | semidirect |
| 9. #22551551 | C2 | semidirect |
| 10. #22551550 | C2 | semidirect |
| 11. C22⋊Q8×C257 | C2 | semidirect |
| 72. C257 | #556 | semidirect |
| 79. C22⋊Q8 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22551591 | 2 |
| #22551587 | 2 |
| #22551585 | 2 |
| #22551578 | 2 |
| #22551568 | 2 |
| Q8×Dic257 | 2 |
| #22551557 | 2 |
| C4×C22⋊D257 | 2 |
| #22551551 | 2 |
| #22551550 | 2 |
| C22⋊Q8×C257 | 2 |
| #556 | 257 |