Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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×#22575478 | C2 | semidirect |
| 2. C22×#16864389 | C2 | semidirect |
| 3. #31771169 | C2 | semidirect |
| 4. #31770750 | C2 | semidirect |
| 5. #31770744 | C2 | semidirect |
| 6. #31770614 | C2 | semidirect |
| 7. #31770601 | C2 | semidirect |
| 8. #31770572 | C2 | semidirect |
| 9. C2×2−1+4×C269 | C2 | semidirect |
| 23. #22575377 | C22 | semidirect |
| 24. #22575377 | C22 | semidirect |
| 25. #22575374 | C22 | semidirect |
| 26. C22⋊#14524130 | C22 | semidirect |
| 33. C2×#41×C269 | C22 | semidirect |
| 36. C22×Q8×C269 | C22 | semidirect |
| 61. #41×C269 | D4 | semidirect |
| 69. C2×Q8×C269 | D4 | semidirect |
| 145. C269 | #3010 | semidirect |
| 147. C2×2−1+4 | D269 | semidirect |
| 162. C2×#41 | C2×D269 | semidirect |
| 165. C22×Q8 | C2×D269 | semidirect |
| 191. #41 | C22⋊D269 | semidirect |
| 199. C2×Q8 | C22⋊D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575478 | 2 |
| C22×#16864389 | 2 |
| #31771169 | 2 |
| #31770750 | 2 |
| #31770744 | 2 |
| #31770614 | 2 |
| #31770601 | 2 |
| #31770572 | 2 |
| C2×2−1+4×C269 | 2 |
| #3010 | 269 |