Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 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. C22×#16864389 | C2 | semidirect |
| 4. #31770827 | C2 | semidirect |
| 5. #31770805 | C2 | semidirect |
| 6. #31770632 | C2 | semidirect |
| 7. #31770609 | C2 | semidirect |
| 8. #31770599 | C2 | semidirect |
| 9. #519×C269 | C2 | semidirect |
| 13. C2×#16864392 | C22 | semidirect |
| 16. C2×#16864389 | C22 | semidirect |
| 23. C4⋊#14524130 | C22 | semidirect |
| 24. #22575376 | C22 | semidirect |
| 26. #22575373 | C22 | semidirect |
| 29. C4×Q8×C269 | C22 | semidirect |
| 55. C2×Q8×C269 | D4 | semidirect |
| 116. C269 | #3043 | semidirect |
| 121. #519 | D269 | semidirect |
| 142. C4×Q8 | C2×D269 | semidirect |
| 156. C2×Q8 | D1076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575484 | 2 |
| C22×#16864389 | 2 |
| #31771174 | 2 |
| #31770827 | 2 |
| #31770805 | 2 |
| #31770632 | 2 |
| #31770609 | 2 |
| #31770599 | 2 |
| #519×C269 | 2 |
| #3043 | 269 |