Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
298 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 148 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. C2×#16861628 | C2 | semidirect |
| 2. D257⋊M16 | C2 | direct (N × H) |
| 3. C2×#16861627 | C2 | semidirect |
| 4. C2×#16861626 | C2 | semidirect |
| 6. #16861628 | C22 | semidirect |
| 7. #16861627 | C22 | semidirect |
| 8. #16861626 | C22 | semidirect |
| 9. C2×#14523346 | C22 | semidirect |
| 19. #14523346 | C23 | semidirect |
| 43. C2×D257 | M16 | semidirect |
| 52. C2×C257 | C2×M16 | semidirect |
| 55. D257 | C2×M16 | semidirect |
| 56. C257 | C22×M16 | semidirect |
| 111. C2 | D257⋊M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861628 | 2 |
| D257⋊M16 | 2 |
| C2×#16861627 | 2 |
| C2×#16861626 | 2 |
| C22×C4×D257 | 2 |
| C22×M16 | 257 |