Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. #31770713 | C2 | semidirect |
| 4. #31770712 | C2 | semidirect |
| 5. #31770711 | C2 | semidirect |
| 6. C4×#16864392 | C2 | semidirect |
| 7. #31770697 | C2 | semidirect |
| 11. #441×C269 | C2 | semidirect |
| 15. Q16×D269 | C4 | semidirect |
| 108. C269 | #2950 | semidirect |
| 115. #441 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D269 | 2 |
| #31771081 | 2 |
| #31770713 | 2 |
| #31770712 | 2 |
| #31770711 | 2 |
| C4×#16864392 | 2 |
| #31770697 | 2 |
| #31770640 | 2 |
| #31770612 | 2 |
| #31770562 | 2 |
| #441×C269 | 2 |
| #2950 | 269 |