Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31771320 | C2 | semidirect |
| 2. #31770951 | C2 | semidirect |
| 3. #31770926 | C2 | semidirect |
| 4. #31770900 | C2 | semidirect |
| 5. #31770839 | C2 | semidirect |
| 6. #31770797 | C2 | semidirect |
| 7. #31770750 | C2 | semidirect |
| 8. C4×#16864389 | C2 | semidirect |
| 9. D4×#14524130 | C2 | semidirect |
| 10. #31770601 | C2 | semidirect |
| 11. #550×C269 | C2 | semidirect |
| 132. C269 | #3305 | semidirect |
| 135. #550 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771320 | 2 |
| #31770951 | 2 |
| #31770926 | 2 |
| #31770900 | 2 |
| #31770839 | 2 |
| #31770797 | 2 |
| #31770750 | 2 |
| C4×#16864389 | 2 |
| D4×#14524130 | 2 |
| #31770601 | 2 |
| #550×C269 | 2 |
| #3305 | 269 |