Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
740 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×#22575415 | C2 | semidirect |
| 3. #31770506 | C2 | semidirect |
| 4. #31770483 | C2 | semidirect |
| 5. #31770451 | C2 | semidirect |
| 6. #382×C269 | C2 | semidirect |
| 10. #22575450 | C4 | semidirect |
| 24. C2×D1076 | C2×C4 | semidirect |
| 25. C2×D1076 | C2×C4 | semidirect |
| 33. C4×Dic269 | D4 | semidirect |
| 38. C42×C269 | C2×C4 | semidirect |
| 78. C269 | #2328 | semidirect |
| 84. #382 | D269 | semidirect |
| 117. C42 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575450 | 2 |
| C2×#22575415 | 2 |
| #31770506 | 2 |
| #31770483 | 2 |
| #31770451 | 2 |
| #382×C269 | 2 |
| #2328 | 269 |