Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31771413 | C2 | semidirect |
| 2. #31771407 | C2 | semidirect |
| 3. #31770990 | C2 | semidirect |
| 4. #31770877 | C2 | semidirect |
| 5. #31770875 | C2 | semidirect |
| 6. #31770870 | C2 | semidirect |
| 7. #31770781 | C2 | semidirect |
| 8. #31770778 | C2 | semidirect |
| 9. #31770722 | C2 | semidirect |
| 10. #31770720 | C2 | semidirect |
| 11. #578×C269 | C2 | semidirect |
| 18. #22575478 | C22 | semidirect |
| 23. C2×#16864389 | C22 | semidirect |
| 26. #22575460 | C22 | semidirect |
| 28. #22575442 | C22 | semidirect |
| 29. #22575389 | C22 | semidirect |
| 30. #22575388 | C22 | semidirect |
| 31. #22575380 | C22 | semidirect |
| 32. #22575380 | C22 | semidirect |
| 34. #22575372 | C22 | semidirect |
| 35. #22575369 | C22 | semidirect |
| 36. C8×Dic269 | C22 | semidirect |
| 37. 2−1+4×C269 | C22 | semidirect |
| 39. #137×C269 | C22 | semidirect |
| 43. C2×Q16×C269 | C22 | semidirect |
| 44. #131×C269 | C22 | semidirect |
| 149. C269 | #3290 | semidirect |
| 151. #578 | D269 | semidirect |
| 162. 2−1+4 | C2×D269 | semidirect |
| 167. #137 | C2×D269 | semidirect |
| 178. C2×Q16 | C2×D269 | semidirect |
| 185. #131 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771413 | 2 |
| #31771407 | 2 |
| #31770990 | 2 |
| #31770877 | 2 |
| #31770875 | 2 |
| #31770870 | 2 |
| #31770781 | 2 |
| #31770778 | 2 |
| #31770722 | 2 |
| #31770720 | 2 |
| #578×C269 | 2 |
| #3290 | 269 |