Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 2. #31771082 | C2 | semidirect |
| 4. #31770707 | C2 | semidirect |
| 5. C4×#16864391 | C2 | semidirect |
| 6. #31770643 | C2 | semidirect |
| 7. #31770615 | C2 | semidirect |
| 9. #405×C269 | C2 | semidirect |
| 12. C2×#16864391 | C4 | semidirect |
| 15. C4×Dic538 | C22 | semidirect |
| 23. #22575387 | C22 | semidirect |
| 24. #22575385 | C22 | semidirect |
| 25. #22575378 | C22 | semidirect |
| 30. #97×C269 | C22 | semidirect |
| 31. C4×C8×C269 | C22 | semidirect |
| 35. C2×Dic538 | C2×C4 | semidirect |
| 43. #16864391 | C2×C4 | semidirect |
| 44. #16864391 | C2×C4 | semidirect |
| 56. C2×C8×C269 | C2×C4 | semidirect |
| 103. C269 | #2949 | semidirect |
| 113. #405 | D269 | semidirect |
| 134. #97 | C2×D269 | semidirect |
| 135. C4×C8 | C2×D269 | semidirect |
| 151. C2×C8 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864391 | 2 |
| #31771082 | 2 |
| #31771079 | 2 |
| #31770707 | 2 |
| C4×#16864391 | 2 |
| #31770643 | 2 |
| #31770615 | 2 |
| #31770611 | 2 |
| #405×C269 | 2 |
| #2949 | 269 |