Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
284 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #31770563 | C2 | semidirect |
| 4. #31770377 | C2 | semidirect |
| 8. C2×#16864386 | C4 | semidirect |
| 10. C22×#14524130 | C4 | semidirect |
| 18. #101×C269 | C4 | semidirect |
| 19. #100×C269 | C4 | semidirect |
| 74. C269 | #1757 | semidirect |
| 90. #101 | Dic269 | semidirect |
| 91. #100 | Dic269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575460 | 2 |
| #31770579 | 2 |
| #31770563 | 2 |
| #31770377 | 2 |
| #413×C269 | 2 |
| #1757 | 269 |