Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
652 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 213 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×Q8×Dic269 | C2 | semidirect |
| 5. #31770497 | C2 | semidirect |
| 6. #31770470 | C2 | semidirect |
| 7. #31770452 | C2 | semidirect |
| 8. C42×Dic269 | C2 | semidirect |
| 9. #391×C269 | C2 | semidirect |
| 12. #22575442 | C4 | semidirect |
| 44. #16864379 | C2×C4 | semidirect |
| 48. C4×Dic269 | C2×C4 | semidirect |
| 52. C2×Q8×C269 | C2×C4 | semidirect |
| 105. Dic269 | #124 | semidirect |
| 112. C269 | C4×#124 | semidirect |
| 117. #391 | D269 | semidirect |
| 146. C2×Q8 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575442 | 2 |
| C2×Q8×Dic269 | 2 |
| C2×#22575415 | 2 |
| #31770507 | 2 |
| #31770497 | 2 |
| #31770470 | 2 |
| #31770452 | 2 |
| C42×Dic269 | 2 |
| #391×C269 | 2 |
| C4×#124 | 269 |