Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#22575477 | C2 | semidirect |
| 2. #31771153 | C2 | semidirect |
| 3. C4×D4×D269 | C2 | semidirect |
| 4. #31770819 | C2 | semidirect |
| 5. #31770818 | C2 | semidirect |
| 6. #31770811 | C2 | semidirect |
| 7. #31770810 | C2 | semidirect |
| 8. #31770797 | C2 | semidirect |
| 9. #31770627 | C2 | semidirect |
| 10. #31770603 | C2 | semidirect |
| 11. #459×C269 | C2 | semidirect |
| 20. #22575453 | C22 | semidirect |
| 21. #22575440 | C22 | semidirect |
| 34. C4⋊#14524130 | C22 | semidirect |
| 35. #22575382 | C22 | semidirect |
| 36. #22575378 | C22 | semidirect |
| 37. #22575376 | C22 | semidirect |
| 38. #22575374 | C22 | semidirect |
| 40. #127×C269 | C22 | semidirect |
| 42. C4⋊C8×C269 | C22 | semidirect |
| 43. #102×C269 | C22 | semidirect |
| 52. D4×D269 | D4 | semidirect |
| 145. C4×C269 | AGL(1,ℤ/8) | semidirect |
| 160. C269 | #3036 | semidirect |
| 170. #459 | D269 | semidirect |
| 183. #127 | C2×D269 | semidirect |
| 200. C4⋊C8 | C2×D269 | semidirect |
| 204. #102 | C2×D269 | semidirect |
| 311. C4 | #22575477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575477 | 2 |
| #31771153 | 2 |
| C4×D4×D269 | 2 |
| #31770819 | 2 |
| #31770818 | 2 |
| #31770811 | 2 |
| #31770810 | 2 |
| #31770797 | 2 |
| #31770627 | 2 |
| #31770603 | 2 |
| #459×C269 | 2 |
| #3036 | 269 |