Finite Group DatabasebetaFinite Group DatabasebetaOrder 16832.
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 |
|---|---|---|
| 2. C4×Dic526 | C2 | semidirect |
| 3. #22554403 | C2 | semidirect |
| 4. #22554393 | C2 | semidirect |
| 6. #22554381 | C2 | semidirect |
| 9. #16862364 | C4 | semidirect |
| 21. Dic526 | C2×C4 | semidirect |
| 25. C263⋊C8 | C2×C4 | semidirect |
| 49. C263 | #440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862364 | 2 |
| C4×Dic526 | 2 |
| #22554403 | 2 |
| #22554393 | 2 |
| #22554391 | 2 |
| #22554381 | 2 |
| C4×D4×C263 | 2 |
| #440 | 263 |