Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31771404 | C2 | semidirect |
| 2. C2×#22575476 | C2 | semidirect |
| 3. #131×D269 | C2 | semidirect |
| 4. #31770877 | C2 | semidirect |
| 5. #31770876 | C2 | semidirect |
| 6. #31770875 | C2 | semidirect |
| 7. #31770871 | C2 | semidirect |
| 8. #31770870 | C2 | semidirect |
| 9. #108×D269 | C2 | semidirect |
| 10. #31770588 | C2 | semidirect |
| 11. #473×C269 | C2 | semidirect |
| 25. C2×#16864389 | C22 | semidirect |
| 26. C2×D2152 | C22 | semidirect |
| 37. #22575389 | C22 | semidirect |
| 38. #22575388 | C22 | semidirect |
| 39. #22575372 | C22 | semidirect |
| 40. #22575369 | C22 | semidirect |
| 41. #22575369 | C22 | semidirect |
| 43. C2×Q16×C269 | C22 | semidirect |
| 45. #108×C269 | C22 | semidirect |
| 46. #101×C269 | C22 | semidirect |
| 166. C269 | #3067 | semidirect |
| 172. #473 | D269 | semidirect |
| 193. C2×Q16 | C2×D269 | semidirect |
| 209. #108 | C2×D269 | semidirect |
| 211. #101 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771404 | 2 |
| C2×#22575476 | 2 |
| #131×D269 | 2 |
| #31770877 | 2 |
| #31770876 | 2 |
| #31770875 | 2 |
| #31770871 | 2 |
| #31770870 | 2 |
| #108×D269 | 2 |
| #31770588 | 2 |
| #473×C269 | 2 |
| #3067 | 269 |