Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 173 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. #31770485 | C2 | semidirect |
| 3. #31770484 | C2 | semidirect |
| 4. #31770483 | C2 | semidirect |
| 5. #31770482 | C2 | semidirect |
| 6. #31770481 | C2 | semidirect |
| 7. #31770481 | C2 | semidirect |
| 8. #31770472 | C2 | semidirect |
| 9. #386×C269 | C2 | semidirect |
| 15. #22575449 | C4 | semidirect |
| 35. C2×D1076 | C2×C4 | semidirect |
| 40. C2×C22⋊D269 | C2×C4 | semidirect |
| 41. C2×C22⋊D269 | C2×C4 | semidirect |
| 55. C4×Dic269 | C2×C4 | semidirect |
| 60. C2×D4×C269 | C2×C4 | semidirect |
| 147. C269 | #2380 | semidirect |
| 156. #386 | D269 | semidirect |
| 194. C2×D4 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575449 | 2 |
| #31770485 | 2 |
| #31770484 | 2 |
| #31770483 | 2 |
| #31770482 | 2 |
| #31770481 | 2 |
| #31770472 | 2 |
| #386×C269 | 2 |
| #2380 | 269 |