Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4×Q8×D269 | C2 | semidirect |
| 3. #31770917 | C2 | semidirect |
| 4. #31770901 | C2 | semidirect |
| 5. #31770900 | C2 | semidirect |
| 6. #31770802 | C2 | semidirect |
| 7. #31770742 | C2 | semidirect |
| 8. #31770706 | C2 | semidirect |
| 9. #31770702 | C2 | semidirect |
| 10. #31770661 | C2 | semidirect |
| 11. #460×C269 | C2 | semidirect |
| 87. Dic538 | #41 | semidirect |
| 105. Q8×C269 | #41 | semidirect |
| 140. C269 | #3112 | semidirect |
| 148. #460 | D269 | semidirect |
| 231. Q8 | #16864401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771153 | 2 |
| C4×Q8×D269 | 2 |
| #31770917 | 2 |
| #31770901 | 2 |
| #31770900 | 2 |
| #31770802 | 2 |
| #31770742 | 2 |
| #31770706 | 2 |
| #31770702 | 2 |
| #31770661 | 2 |
| #460×C269 | 2 |
| #3112 | 269 |