Finite Group DatabasebetaFinite Group DatabasebetaOrder 16832.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22554469 | C2 | semidirect |
| 2. #22554468 | C2 | semidirect |
| 3. #22554465 | C2 | semidirect |
| 4. #22554465 | C2 | semidirect |
| 5. #22554463 | C2 | semidirect |
| 6. #22554463 | C2 | semidirect |
| 7. #22554461 | C2 | semidirect |
| 8. #22554460 | C2 | semidirect |
| 12. #22554449 | C2 | semidirect |
| 13. #22554448 | C2 | semidirect |
| 14. #22554446 | C2 | semidirect |
| 15. C22⋊Q8×C263 | C2 | semidirect |
| 97. C263 | #563 | semidirect |
| 113. C22⋊Q8 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554469 | 2 |
| #22554468 | 2 |
| #22554465 | 2 |
| #22554463 | 2 |
| #22554461 | 2 |
| #22554460 | 2 |
| #22554456 | 2 |
| #22554453 | 2 |
| #22554452 | 2 |
| #22554449 | 2 |
| #22554448 | 2 |
| #22554446 | 2 |
| C22⋊Q8×C263 | 2 |
| #563 | 263 |