Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
778 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 293 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×#22575460 | C2 | semidirect |
| 2. #31771088 | C2 | semidirect |
| 3. #31770610 | C2 | semidirect |
| 4. #31770606 | C2 | semidirect |
| 5. #31770601 | C2 | semidirect |
| 6. C2×#22575374 | C2 | semidirect |
| 9. C2×#16864386 | C22 | semidirect |
| 10. C22×#14524130 | C22 | semidirect |
| 13. #22575412 | C22 | semidirect |
| 14. C2×C4⋊Dic269 | C22 | semidirect |
| 15. #22575377 | C22 | semidirect |
| 16. #22575377 | C22 | semidirect |
| 17. #22575374 | C22 | semidirect |
| 18. #22575374 | C22 | semidirect |
| 19. #22575374 | C22 | semidirect |
| 21. H(5,𝔽2)×C269 | C4 | semidirect |
| 41. #41×C269 | C2×C4 | semidirect |
| 49. C2×D4×C269 | C2×C4 | semidirect |
| 97. C269 | #2897 | semidirect |
| 107. H(5,𝔽2) | Dic269 | semidirect |
| 129. #41 | C2×Dic269 | semidirect |
| 137. C2×D4 | C2×Dic269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575460 | 2 |
| #31771088 | 2 |
| #31770610 | 2 |
| #31770606 | 2 |
| #31770601 | 2 |
| C2×#22575374 | 2 |
| C2×H(5,𝔽2)×C269 | 2 |
| #2897 | 269 |