Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
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. #22551587 | C2 | semidirect |
| 2. #22551583 | C2 | semidirect |
| 3. #22551582 | C2 | semidirect |
| 5. #22551572 | C2 | semidirect |
| 6. #22551571 | C2 | semidirect |
| 7. #22551557 | C2 | semidirect |
| 9. #22551551 | C2 | semidirect |
| 10. #22551550 | C2 | semidirect |
| 11. C2×C4⋊C4×C257 | C2 | semidirect |
| 72. C257 | #552 | semidirect |
| 84. C2×C4⋊C4 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22551587 | 2 |
| #22551583 | 2 |
| #22551582 | 2 |
| #22551575 | 2 |
| #22551572 | 2 |
| #22551571 | 2 |
| #22551557 | 2 |
| C4×C22⋊D257 | 2 |
| #22551551 | 2 |
| #22551550 | 2 |
| C2×C4⋊C4×C257 | 2 |
| #552 | 257 |