Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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×#22575481 | C2 | semidirect |
| 2. C2×#22575478 | C2 | semidirect |
| 3. #31771151 | C2 | semidirect |
| 4. C2×#22575415 | C2 | semidirect |
| 5. #31770823 | C2 | semidirect |
| 6. #31770819 | C2 | semidirect |
| 7. #31770809 | C2 | semidirect |
| 8. #31770799 | C2 | semidirect |
| 9. #31770628 | C2 | semidirect |
| 10. #31770604 | C2 | semidirect |
| 11. #417×C269 | C2 | semidirect |
| 22. #22575451 | C22 | semidirect |
| 23. #22575449 | C22 | semidirect |
| 24. #22575442 | C22 | semidirect |
| 25. #22575440 | C22 | semidirect |
| 36. #22575382 | C22 | semidirect |
| 37. #22575382 | C22 | semidirect |
| 38. #22575376 | C22 | semidirect |
| 39. #22575373 | C22 | semidirect |
| 43. #103×C269 | C22 | semidirect |
| 44. #102×C269 | C22 | semidirect |
| 51. C2×D1076 | D4 | semidirect |
| 158. Dic269 | AGL(1,ℤ/8) | semidirect |
| 166. C269 | #3036 | semidirect |
| 178. #417 | D269 | semidirect |
| 209. #103 | C2×D269 | semidirect |
| 211. #102 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575481 | 2 |
| C2×#22575478 | 2 |
| #31771151 | 2 |
| C2×#22575415 | 2 |
| #31770823 | 2 |
| #31770819 | 2 |
| #31770809 | 2 |
| #31770799 | 2 |
| #31770628 | 2 |
| #31770604 | 2 |
| #417×C269 | 2 |
| #3036 | 269 |