Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 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. #31770512 | C2 | semidirect |
| 3. #31770497 | C2 | semidirect |
| 4. #31770495 | C2 | semidirect |
| 6. C4×#16864379 | C2 | semidirect |
| 7. #31770452 | C2 | semidirect |
| 8. #31770450 | C2 | semidirect |
| 9. #391×C269 | C2 | semidirect |
| 12. #22575442 | C4 | semidirect |
| 46. #16864379 | C2×C4 | semidirect |
| 47. #16864379 | C2×C4 | semidirect |
| 51. C4×Dic269 | C2×C4 | semidirect |
| 54. C2×Q8×C269 | C2×C4 | semidirect |
| 123. C269 | #2372 | semidirect |
| 127. #391 | D269 | semidirect |
| 159. C2×Q8 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575442 | 2 |
| #31770512 | 2 |
| #31770497 | 2 |
| #31770495 | 2 |
| #31770483 | 2 |
| C4×#16864379 | 2 |
| #31770452 | 2 |
| #31770450 | 2 |
| #391×C269 | 2 |
| #2372 | 269 |