Finite Group DatabasebetaFinite Group DatabasebetaOrder 16832.
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. #22554465 | C2 | semidirect |
| 2. #22554463 | C2 | semidirect |
| 3. #22554460 | C2 | semidirect |
| 4. #22554456 | C2 | semidirect |
| 5. #22554454 | C2 | semidirect |
| 6. #22554451 | C2 | semidirect |
| 7. #22554447 | C2 | semidirect |
| 9. C4×Dic526 | C2 | semidirect |
| 10. C4×C22⋊D263 | C2 | semidirect |
| 11. C4×C22⋊D263 | C2 | semidirect |
| 12. #22554429 | C2 | semidirect |
| 13. #22554427 | C2 | semidirect |
| 14. C2×C4×Dic263 | C2 | semidirect |
| 15. C4×D4×C263 | C2 | semidirect |
| 103. C263 | #529 | semidirect |
| 116. C4×D4 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554465 | 2 |
| #22554463 | 2 |
| #22554460 | 2 |
| #22554456 | 2 |
| #22554454 | 2 |
| #22554451 | 2 |
| #22554447 | 2 |
| #22554442 | 2 |
| C4×Dic526 | 2 |
| C4×C22⋊D263 | 2 |
| #22554429 | 2 |
| #22554427 | 2 |
| C2×C4×Dic263 | 2 |
| C4×D4×C263 | 2 |
| #529 | 263 |