Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22551585 | C2 | semidirect |
| 2. #22551583 | C2 | semidirect |
| 3. #22551579 | C2 | semidirect |
| 4. #22551574 | C2 | semidirect |
| 5. #22551572 | C2 | semidirect |
| 7. C4×Dic514 | C2 | semidirect |
| 8. C4×C22⋊D257 | C2 | semidirect |
| 9. #22551551 | C2 | semidirect |
| 10. C42×D257 | C2 | semidirect |
| 11. C4×D4×C257 | C2 | semidirect |
| 74. C257 | #529 | semidirect |
| 84. C4×D4 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22551585 | 2 |
| #22551583 | 2 |
| #22551579 | 2 |
| #22551574 | 2 |
| #22551572 | 2 |
| #22551563 | 2 |
| C4×Dic514 | 2 |
| C4×C22⋊D257 | 2 |
| #22551551 | 2 |
| C42×D257 | 2 |
| C4×D4×C257 | 2 |
| #529 | 257 |