Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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×#22575479 | C2 | semidirect |
| 2. #31771155 | C2 | semidirect |
| 3. #31770820 | C2 | semidirect |
| 4. #31770810 | C2 | semidirect |
| 5. #31770800 | C2 | semidirect |
| 6. #31770629 | C2 | semidirect |
| 7. #31770604 | C2 | semidirect |
| 8. C2×C4×D4×C269 | C2 | semidirect |
| 14. #22575453 | C22 | semidirect |
| 15. #22575450 | C22 | semidirect |
| 16. #22575441 | C22 | semidirect |
| 21. C4⋊#14524130 | C22 | semidirect |
| 22. C4⋊#14524130 | C22 | semidirect |
| 23. #22575376 | C22 | semidirect |
| 24. #22575373 | C22 | semidirect |
| 53. C2×D4×C269 | D4 | semidirect |
| 119. C4×C269 | AGL(1,ℤ/8) | semidirect |
| 129. C269 | #3036 | semidirect |
| 133. C2×C4×D4 | D269 | semidirect |
| 174. C2×D4 | D1076 | semidirect |
| 250. C4 | #22575479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575479 | 2 |
| #31771155 | 2 |
| #31770820 | 2 |
| #31770810 | 2 |
| #31770800 | 2 |
| #31770629 | 2 |
| #31770604 | 2 |
| C2×C4×D4×C269 | 2 |
| #3036 | 269 |