Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 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. #31771420 | C2 | semidirect |
| 2. #31771419 | C2 | semidirect |
| 3. #31770983 | C2 | semidirect |
| 4. #31770880 | C2 | semidirect |
| 5. #31770878 | C2 | semidirect |
| 6. #31770877 | C2 | semidirect |
| 7. #31770788 | C2 | semidirect |
| 8. #31770786 | C2 | semidirect |
| 9. #31770722 | C2 | semidirect |
| 10. #31770720 | C2 | semidirect |
| 11. #578×C269 | C2 | semidirect |
| 146. C269 | #3293 | semidirect |
| 150. #578 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771420 | 2 |
| #31771419 | 2 |
| #31770983 | 2 |
| #31770880 | 2 |
| #31770878 | 2 |
| #31770877 | 2 |
| #31770788 | 2 |
| #31770786 | 2 |
| #31770722 | 2 |
| #31770720 | 2 |
| #578×C269 | 2 |
| #3293 | 269 |