Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#22575486 | C2 | semidirect |
| 3. #31771176 | C2 | semidirect |
| 4. #31770790 | C2 | semidirect |
| 5. #31770785 | C2 | semidirect |
| 6. #31770621 | C2 | semidirect |
| 7. #413×C269 | C2 | semidirect |
| 16. C22×Dic538 | C22 | semidirect |
| 18. #22575486 | C22 | semidirect |
| 21. #22575451 | C22 | semidirect |
| 22. #22575440 | C22 | semidirect |
| 25. #22575412 | C22 | semidirect |
| 26. #22575379 | C22 | semidirect |
| 28. C2×M16×C269 | C22 | semidirect |
| 29. #101×C269 | C22 | semidirect |
| 30. #100×C269 | C22 | semidirect |
| 129. C269 | #3022 | semidirect |
| 137. #413 | D269 | semidirect |
| 152. C2×M16 | C2×D269 | semidirect |
| 159. #101 | C2×D269 | semidirect |
| 160. #100 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771441 | 2 |
| C2×#22575486 | 2 |
| #31771176 | 2 |
| #31770790 | 2 |
| #31770785 | 2 |
| #31770621 | 2 |
| #413×C269 | 2 |
| #3022 | 269 |