Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
444 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31771422 | C2 | semidirect |
| 2. #31771421 | C2 | semidirect |
| 3. #31771418 | C2 | semidirect |
| 4. #31770983 | C2 | semidirect |
| 5. #31770881 | C2 | semidirect |
| 6. #31770879 | C2 | semidirect |
| 7. #31770790 | C2 | semidirect |
| 8. #31770786 | C2 | semidirect |
| 9. #31770721 | C2 | semidirect |
| 10. #31770720 | C2 | semidirect |
| 11. #473×C269 | C2 | semidirect |
| 146. C269 | #3293 | semidirect |
| 154. #473 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771422 | 2 |
| #31771421 | 2 |
| #31771418 | 2 |
| #31770983 | 2 |
| #31770881 | 2 |
| #31770879 | 2 |
| #31770790 | 2 |
| #31770786 | 2 |
| #31770721 | 2 |
| #31770720 | 2 |
| #473×C269 | 2 |
| #3293 | 269 |