Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
| 3. C4×#16864402 | C2 | semidirect |
| 4. #31770824 | C2 | semidirect |
| 5. #31770817 | C2 | semidirect |
| 6. #31770629 | C2 | semidirect |
| 7. #31770614 | C2 | semidirect |
| 8. #31770610 | C2 | semidirect |
| 9. C2×#124×C269 | C2 | semidirect |
| 13. C2×#16864392 | C22 | semidirect |
| 15. C2×#16864389 | C22 | semidirect |
| 19. C4×Dic538 | C22 | semidirect |
| 20. C4×D1076 | C22 | semidirect |
| 25. C4⋊#14524130 | C22 | semidirect |
| 26. #22575377 | C22 | semidirect |
| 125. C269 | #3040 | semidirect |
| 129. C2×#124 | 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×#22575479 | 2 |
| C4×#16864402 | 2 |
| #31770824 | 2 |
| #31770817 | 2 |
| #31770629 | 2 |
| #31770614 | 2 |
| #31770610 | 2 |
| C2×#124×C269 | 2 |
| #3040 | 269 |