Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22575460 | C2 | semidirect |
| 3. #31771169 | C2 | semidirect |
| 4. #31770856 | C2 | semidirect |
| 5. #31770839 | C2 | semidirect |
| 6. #31770641 | C2 | semidirect |
| 7. #31770610 | C2 | semidirect |
| 8. #31770609 | C2 | semidirect |
| 9. #535×C269 | C2 | semidirect |
| 16. C2×#16864386 | C22 | semidirect |
| 18. C22×#14524130 | C22 | semidirect |
| 21. #22575427 | C22 | semidirect |
| 24. #22575386 | C22 | semidirect |
| 25. #22575384 | C22 | semidirect |
| 26. #22575374 | C22 | semidirect |
| 27. #22575373 | C22 | semidirect |
| 32. #121×C269 | C22 | semidirect |
| 46. C2×#14524130 | D4 | semidirect |
| 125. C269 | #3058 | semidirect |
| 130. #535 | D269 | semidirect |
| 152. #121 | 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×#22575460 | 2 |
| #31771169 | 2 |
| #31770856 | 2 |
| #31770839 | 2 |
| #31770641 | 2 |
| #31770610 | 2 |
| #31770609 | 2 |
| #535×C269 | 2 |
| #3058 | 269 |