Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #31770704 | C2 | semidirect |
| 5. #31770692 | C2 | semidirect |
| 6. #31770613 | C2 | semidirect |
| 8. #31770560 | C2 | semidirect |
| 9. #427×C269 | C2 | semidirect |
| 12. C2×#16864391 | C4 | semidirect |
| 17. #22575418 | C22 | semidirect |
| 23. #22575376 | C22 | semidirect |
| 25. #22575363 | C22 | semidirect |
| 26. C8×Dic269 | C22 | semidirect |
| 30. #107×C269 | C22 | semidirect |
| 31. #106×C269 | C22 | semidirect |
| 35. C2×Dic538 | C2×C4 | semidirect |
| 43. #16864391 | C2×C4 | semidirect |
| 44. #16864391 | C2×C4 | semidirect |
| 54. C2×C8×C269 | C2×C4 | semidirect |
| 103. C269 | #2949 | semidirect |
| 110. #427 | D269 | semidirect |
| 130. #107 | C2×D269 | semidirect |
| 131. #106 | C2×D269 | semidirect |
| 152. 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 |
| #31770704 | 2 |
| #31770692 | 2 |
| #31770613 | 2 |
| #31770609 | 2 |
| #31770560 | 2 |
| #427×C269 | 2 |
| #2949 | 269 |