Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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×#22575484 | C2 | semidirect |
| 2. C2×#22575478 | C2 | semidirect |
| 3. C2×#22575473 | C2 | semidirect |
| 4. C22×#16864389 | C2 | semidirect |
| 5. #31771174 | C2 | semidirect |
| 6. #31770997 | C2 | semidirect |
| 7. #31770995 | C2 | semidirect |
| 8. #31770987 | C2 | semidirect |
| 9. #31770979 | C2 | semidirect |
| 10. #31770561 | C2 | semidirect |
| 11. #536×C269 | C2 | semidirect |
| 17. C2×#16864392 | C22 | semidirect |
| 18. C2×#16864392 | C22 | semidirect |
| 19. C2×#16864390 | C22 | semidirect |
| 24. C2×#16864389 | C22 | semidirect |
| 25. C2×#16864389 | C22 | semidirect |
| 27. C2×#16864387 | C22 | semidirect |
| 34. #22575364 | C22 | semidirect |
| 35. C4×#14524130 | C22 | semidirect |
| 38. C4⋊Q8×C269 | C22 | semidirect |
| 39. #124×C269 | C22 | semidirect |
| 65. #16864386 | D4 | semidirect |
| 66. C2×#14524130 | D4 | semidirect |
| 148. C269 | #3154 | semidirect |
| 154. #536 | D269 | semidirect |
| 181. C4⋊Q8 | C2×D269 | semidirect |
| 184. #124 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575484 | 2 |
| C2×#22575478 | 2 |
| C2×#22575473 | 2 |
| C22×#16864389 | 2 |
| #31771174 | 2 |
| #31770997 | 2 |
| #31770995 | 2 |
| #31770987 | 2 |
| #31770979 | 2 |
| #31770561 | 2 |
| #536×C269 | 2 |
| #3154 | 269 |