Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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. #31771259 | C2 | semidirect |
| 2. #31770951 | C2 | semidirect |
| 3. #31770916 | C2 | semidirect |
| 4. #31770885 | C2 | semidirect |
| 5. #31770839 | C2 | semidirect |
| 6. #31770797 | C2 | semidirect |
| 7. #31770739 | C2 | semidirect |
| 8. C4×#16864387 | C2 | semidirect |
| 9. D4×#14524130 | C2 | semidirect |
| 10. C2×#22575374 | C2 | semidirect |
| 11. D42×C269 | C2 | semidirect |
| 14. C2×#16864387 | C22 | semidirect |
| 15. C22×#14524130 | C22 | semidirect |
| 16. #22575453 | C22 | semidirect |
| 19. #22575427 | C22 | semidirect |
| 20. C4×D1076 | C22 | semidirect |
| 21. C2×C4⋊Dic269 | C22 | semidirect |
| 22. #22575386 | C22 | semidirect |
| 23. #22575386 | C22 | semidirect |
| 24. C4⋊#14524130 | C22 | semidirect |
| 27. #22575374 | C22 | semidirect |
| 28. #22575374 | C22 | semidirect |
| 29. #22575374 | C22 | semidirect |
| 30. #22575373 | C22 | semidirect |
| 31. C22⋊#14524130 | C22 | semidirect |
| 32. C4×#14524130 | C22 | semidirect |
| 103. D4×C269 | D8 | semidirect |
| 104. D4×C269 | #41 | semidirect |
| 142. C269 | #3294 | semidirect |
| 145. D42 | D269 | semidirect |
| 239. D4 | #16864387 | semidirect |
| 240. D4 | #16864401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771259 | 2 |
| #31770951 | 2 |
| #31770916 | 2 |
| #31770885 | 2 |
| #31770839 | 2 |
| #31770797 | 2 |
| #31770739 | 2 |
| C4×#16864387 | 2 |
| D4×#14524130 | 2 |
| C2×#22575374 | 2 |
| D42×C269 | 2 |
| #3294 | 269 |