Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22551581 | C2 | semidirect |
| 4. #22551578 | C2 | semidirect |
| 5. #22551574 | C2 | semidirect |
| 6. #22551572 | C2 | semidirect |
| 8. Q8×Dic257 | C2 | semidirect |
| 9. #22551554 | C2 | semidirect |
| 10. #22551551 | C2 | semidirect |
| 11. C22⋊Q8×C257 | C2 | semidirect |
| 73. C257 | #542 | semidirect |
| 81. 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 |
| #22551581 | 2 |
| #22551578 | 2 |
| #22551574 | 2 |
| #22551572 | 2 |
| #22551566 | 2 |
| Q8×Dic257 | 2 |
| #22551554 | 2 |
| #22551551 | 2 |
| C22⋊Q8×C257 | 2 |
| #542 | 257 |