Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 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. #31771236 | C2 | semidirect |
| 3. #31770907 | C2 | semidirect |
| 4. #31770903 | C2 | semidirect |
| 5. #31770893 | C2 | semidirect |
| 6. #31770883 | C2 | semidirect |
| 7. #31770645 | C2 | semidirect |
| 8. #31770643 | C2 | semidirect |
| 9. #31770631 | C2 | semidirect |
| 14. #22575452 | C22 | semidirect |
| 16. #22575444 | C22 | semidirect |
| 26. #22575387 | C22 | semidirect |
| 27. #22575387 | C22 | semidirect |
| 28. #22575386 | C22 | semidirect |
| 29. #22575385 | C22 | semidirect |
| 30. #22575385 | C22 | semidirect |
| 31. #22575384 | C22 | semidirect |
| 32. #22575382 | C22 | semidirect |
| 33. #22575382 | C22 | semidirect |
| 66. C2×D4×C269 | Q8 | semidirect |
| 124. C269 | #3081 | semidirect |
| 170. C2×D4 | Dic538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771236 | 2 |
| #31771080 | 2 |
| #31770907 | 2 |
| #31770903 | 2 |
| #31770893 | 2 |
| #31770883 | 2 |
| #31770645 | 2 |
| #31770643 | 2 |
| #31770631 | 2 |
| #31770610 | 2 |
| C2×#102×C269 | 2 |
| #3081 | 269 |