Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 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. #22551591 | C2 | semidirect |
| 2. #22551590 | C2 | semidirect |
| 3. #22551587 | C2 | semidirect |
| 4. #22551587 | C2 | semidirect |
| 5. #22551585 | C2 | semidirect |
| 6. #22551585 | C2 | semidirect |
| 7. #22551583 | C2 | semidirect |
| 8. #22551582 | C2 | semidirect |
| 12. #22551571 | C2 | semidirect |
| 13. #22551570 | C2 | semidirect |
| 14. #22551568 | C2 | semidirect |
| 15. C22⋊Q8×C257 | C2 | semidirect |
| 97. C257 | #563 | semidirect |
| 113. 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 |
| #22551590 | 2 |
| #22551587 | 2 |
| #22551585 | 2 |
| #22551583 | 2 |
| #22551582 | 2 |
| #22551578 | 2 |
| #22551575 | 2 |
| #22551574 | 2 |
| #22551571 | 2 |
| #22551570 | 2 |
| #22551568 | 2 |
| C22⋊Q8×C257 | 2 |
| #563 | 257 |