Finite Group DatabasebetaFinite Group DatabasebetaOrder 16832.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×Q8×D263 | C2 | semidirect |
| 3. #22554469 | C2 | semidirect |
| 4. #22554456 | C2 | semidirect |
| 5. #22554455 | C2 | semidirect |
| 6. #22554452 | C2 | semidirect |
| 7. #22554450 | C2 | semidirect |
| 8. #22554449 | C2 | semidirect |
| 9. #22554446 | C2 | semidirect |
| 10. #22554428 | C2 | semidirect |
| 11. C22⋊Q8×C263 | C2 | semidirect |
| 83. C263 | #536 | semidirect |
| 94. C22⋊Q8 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862376 | 2 |
| C2×Q8×D263 | 2 |
| #22554469 | 2 |
| #22554456 | 2 |
| #22554455 | 2 |
| #22554452 | 2 |
| #22554450 | 2 |
| #22554449 | 2 |
| #22554446 | 2 |
| #22554428 | 2 |
| C22⋊Q8×C263 | 2 |
| #536 | 263 |