Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 2. #31771079 | C2 | semidirect |
| 3. #31770715 | C2 | semidirect |
| 4. C4×#16864387 | C2 | semidirect |
| 5. #31770641 | C2 | semidirect |
| 6. #31770610 | C2 | semidirect |
| 7. #31770609 | C2 | semidirect |
| 8. #31770561 | C2 | semidirect |
| 9. #518×C269 | C2 | semidirect |
| 11. C2×#16864387 | C4 | semidirect |
| 16. C4×D1076 | C22 | semidirect |
| 20. #22575386 | C22 | semidirect |
| 21. #22575384 | C22 | semidirect |
| 22. #22575374 | C22 | semidirect |
| 23. #22575373 | C22 | semidirect |
| 24. #22575364 | C22 | semidirect |
| 25. C4×#14524130 | C22 | semidirect |
| 28. C4×D4×C269 | C22 | semidirect |
| 35. C2×D1076 | C2×C4 | semidirect |
| 38. #16864387 | C2×C4 | semidirect |
| 39. #16864387 | C2×C4 | semidirect |
| 41. C2×#14524130 | C2×C4 | semidirect |
| 52. C2×D4×C269 | C2×C4 | semidirect |
| 108. C269 | #2948 | semidirect |
| 112. #518 | D269 | semidirect |
| 129. C4×D4 | C2×D269 | semidirect |
| 149. C2×D4 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864387 | 2 |
| #31771079 | 2 |
| #31770715 | 2 |
| C4×#16864387 | 2 |
| #31770641 | 2 |
| #31770610 | 2 |
| #31770609 | 2 |
| #31770561 | 2 |
| #518×C269 | 2 |
| #2948 | 269 |