Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22575500 | C2 | semidirect |
| 2. C2×#22575478 | C2 | semidirect |
| 3. C22×#16864391 | C2 | semidirect |
| 4. #31771174 | C2 | semidirect |
| 5. #31770751 | C2 | semidirect |
| 6. #31770745 | C2 | semidirect |
| 7. #31770613 | C2 | semidirect |
| 8. #31770571 | C2 | semidirect |
| 9. #416×C269 | C2 | semidirect |
| 15. C2×#16864401 | C22 | semidirect |
| 18. C2×Q8×D269 | C22 | semidirect |
| 30. #22575376 | C22 | semidirect |
| 31. #22575365 | C22 | semidirect |
| 35. #103×C269 | C22 | semidirect |
| 36. #102×C269 | C22 | semidirect |
| 49. C2×Dic538 | D4 | semidirect |
| 72. #41×C269 | D4 | semidirect |
| 145. C269 | #3010 | semidirect |
| 154. #416 | D269 | semidirect |
| 180. #103 | C2×D269 | semidirect |
| 181. #102 | C2×D269 | semidirect |
| 191. #41 | D1076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575500 | 2 |
| C2×#22575478 | 2 |
| C22×#16864391 | 2 |
| #31771174 | 2 |
| #31770751 | 2 |
| #31770745 | 2 |
| #31770613 | 2 |
| #31770571 | 2 |
| #416×C269 | 2 |
| #3010 | 269 |