Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#22575482 | C2 | semidirect |
| 2. C2×#22575477 | C2 | semidirect |
| 3. #31771153 | C2 | semidirect |
| 4. #124×D269 | C2 | semidirect |
| 5. #31771000 | C2 | semidirect |
| 6. #31770999 | C2 | semidirect |
| 7. #31770992 | C2 | semidirect |
| 8. #31770988 | C2 | semidirect |
| 9. #31770986 | C2 | semidirect |
| 10. #31770557 | C2 | semidirect |
| 11. #496×C269 | C2 | semidirect |
| 17. C2×Dic1076 | C22 | semidirect |
| 18. C2×#16864392 | C22 | semidirect |
| 21. C2×#16864390 | C22 | semidirect |
| 24. #22575453 | C22 | semidirect |
| 28. #22575440 | C22 | semidirect |
| 34. #22575364 | C22 | semidirect |
| 35. C8×Dic269 | C22 | semidirect |
| 36. C2×SD16×C269 | C22 | semidirect |
| 38. #127×C269 | C22 | semidirect |
| 40. #97×C269 | C22 | semidirect |
| 62. #16864385 | D4 | semidirect |
| 134. C269 | #3153 | semidirect |
| 143. #496 | D269 | semidirect |
| 157. C2×SD16 | C2×D269 | semidirect |
| 162. #127 | C2×D269 | semidirect |
| 174. #97 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575482 | 2 |
| C2×#22575477 | 2 |
| #31771153 | 2 |
| #124×D269 | 2 |
| #31771000 | 2 |
| #31770999 | 2 |
| #31770992 | 2 |
| #31770988 | 2 |
| #31770986 | 2 |
| #31770557 | 2 |
| #496×C269 | 2 |
| #3153 | 269 |