Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 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×#22575499 | C2 | semidirect |
| 2. C2×#22575481 | C2 | semidirect |
| 3. C22×D2152 | C2 | semidirect |
| 4. #31771169 | C2 | semidirect |
| 5. #31770752 | C2 | semidirect |
| 6. #31770741 | C2 | semidirect |
| 7. #31770611 | C2 | semidirect |
| 8. #31770602 | C2 | semidirect |
| 9. #408×C269 | C2 | semidirect |
| 14. C2×#16864402 | C22 | semidirect |
| 16. C22×D1076 | C22 | semidirect |
| 17. C22×D1076 | C22 | semidirect |
| 21. C2×#16864391 | C22 | semidirect |
| 23. C2×D2152 | C22 | semidirect |
| 24. C2×D2152 | C22 | semidirect |
| 27. #22575427 | C22 | semidirect |
| 29. #22575412 | C22 | semidirect |
| 30. #22575378 | C22 | semidirect |
| 31. #22575375 | C22 | semidirect |
| 32. #22575375 | C22 | semidirect |
| 34. C2×M16×C269 | C22 | semidirect |
| 35. C22×C8×C269 | C22 | semidirect |
| 36. C22⋊C8×C269 | C22 | semidirect |
| 44. #16864402 | D4 | semidirect |
| 54. C2×D1076 | D4 | semidirect |
| 151. C269 | #3008 | semidirect |
| 161. #408 | D269 | semidirect |
| 178. C2×M16 | C2×D269 | semidirect |
| 179. C22×C8 | C2×D269 | semidirect |
| 188. C22⋊C8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575499 | 2 |
| C2×#22575481 | 2 |
| C22×D2152 | 2 |
| #31771169 | 2 |
| #31770752 | 2 |
| #31770741 | 2 |
| #31770611 | 2 |
| #31770602 | 2 |
| #408×C269 | 2 |
| #3008 | 269 |