Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
524 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#16864387 | C2 | semidirect |
| 2. C2×#22575461 | C2 | semidirect |
| 3. #31771174 | C2 | semidirect |
| 4. #31771172 | C2 | semidirect |
| 5. #31770857 | C2 | semidirect |
| 6. #31770840 | C2 | semidirect |
| 7. #31770641 | C2 | semidirect |
| 8. #31770611 | C2 | semidirect |
| 9. #418×C269 | C2 | semidirect |
| 16. C2×#16864385 | C22 | semidirect |
| 18. C2×C8×D269 | C22 | semidirect |
| 23. #22575428 | C22 | semidirect |
| 24. #22575424 | C22 | semidirect |
| 28. #22575386 | C22 | semidirect |
| 29. #22575384 | C22 | semidirect |
| 30. #22575375 | C22 | semidirect |
| 34. #102×C269 | C22 | semidirect |
| 51. C2×#14524130 | D4 | semidirect |
| 125. C269 | #3058 | semidirect |
| 135. #418 | D269 | semidirect |
| 160. #102 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864387 | 2 |
| C2×#22575461 | 2 |
| #31771174 | 2 |
| #31771172 | 2 |
| #31770857 | 2 |
| #31770840 | 2 |
| #31770641 | 2 |
| #31770611 | 2 |
| #418×C269 | 2 |
| #3058 | 269 |