Finite Group DatabasebetaFinite Group DatabasebetaOrder 16832.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 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. #22554465 | C2 | semidirect |
| 2. #22554463 | C2 | semidirect |
| 3. #22554460 | C2 | semidirect |
| 4. #22554456 | C2 | semidirect |
| 5. #22554455 | C2 | semidirect |
| 6. #22554452 | C2 | semidirect |
| 7. #22554448 | C2 | semidirect |
| 9. C4×Dic526 | C2 | semidirect |
| 10. C4×D1052 | C2 | semidirect |
| 11. C4×C22⋊D263 | C2 | semidirect |
| 12. C4×C22⋊D263 | C2 | semidirect |
| 13. #22554427 | C2 | semidirect |
| 14. C42×D263 | C2 | semidirect |
| 15. #117×C263 | C2 | semidirect |
| 103. C263 | #529 | semidirect |
| 118. #117 | 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 |
| #22554455 | 2 |
| #22554452 | 2 |
| #22554448 | 2 |
| #22554443 | 2 |
| C4×Dic526 | 2 |
| C4×D1052 | 2 |
| C4×C22⋊D263 | 2 |
| #22554427 | 2 |
| C42×D263 | 2 |
| #117×C263 | 2 |
| #529 | 263 |