Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 3. #22551525 | C2 | semidirect |
| 4. #22551516 | C2 | semidirect |
| 6. #22551503 | C2 | semidirect |
| 7. C4×Q8×C257 | C2 | semidirect |
| 10. #16861605 | C4 | semidirect |
| 26. #14523339 | C2×C4 | semidirect |
| 28. Q8×C257 | C2×C4 | semidirect |
| 49. C257 | #440 | semidirect |
| 52. C4×Q8 | D257 | semidirect |
| 72. Q8 | C4×D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861605 | 2 |
| C4×D1028 | 2 |
| #22551525 | 2 |
| #22551516 | 2 |
| #22551512 | 2 |
| #22551503 | 2 |
| C4×Q8×C257 | 2 |
| #440 | 257 |