Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 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. C22×#16864389 | C2 | semidirect |
| 3. #31771083 | C2 | semidirect |
| 4. #31770829 | C2 | semidirect |
| 5. #31770803 | C2 | semidirect |
| 6. #31770633 | C2 | semidirect |
| 7. #31770611 | C2 | semidirect |
| 8. #31770601 | C2 | semidirect |
| 9. C2×#137×C269 | C2 | semidirect |
| 19. Q8×Dic269 | C22 | semidirect |
| 23. #22575382 | C22 | semidirect |
| 24. #22575377 | C22 | semidirect |
| 26. #22575374 | C22 | semidirect |
| 30. C2×Q16×C269 | C22 | semidirect |
| 31. C2×SD16×C269 | C22 | semidirect |
| 55. C2×Q8×C269 | D4 | semidirect |
| 116. C269 | #3043 | semidirect |
| 118. C2×#137 | D269 | semidirect |
| 131. C2×Q16 | C2×D269 | semidirect |
| 134. C2×SD16 | C2×D269 | semidirect |
| 155. C2×Q8 | C22⋊D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864389 | 2 |
| #31771169 | 2 |
| #31771083 | 2 |
| #31770829 | 2 |
| #31770803 | 2 |
| #31770633 | 2 |
| #31770611 | 2 |
| #31770601 | 2 |
| C2×#137×C269 | 2 |
| #3043 | 269 |