Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C4⋊Q8×D269 | C2 | semidirect |
| 3. #31770901 | C2 | semidirect |
| 4. #31770897 | C2 | semidirect |
| 5. #31770895 | C2 | semidirect |
| 6. #31770889 | C2 | semidirect |
| 7. #31770883 | C2 | semidirect |
| 8. #31770644 | C2 | semidirect |
| 9. #31770627 | C2 | semidirect |
| 11. #476×C269 | C2 | semidirect |
| 44. #16864401 | Q8 | semidirect |
| 86. Dic538 | C2×Q8 | semidirect |
| 105. D4×C269 | C2×Q8 | semidirect |
| 137. C269 | #3079 | semidirect |
| 144. #476 | D269 | semidirect |
| 229. D4 | Q8×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D269 | 2 |
| C4×#16864401 | 2 |
| #31770901 | 2 |
| #31770897 | 2 |
| #31770895 | 2 |
| #31770889 | 2 |
| #31770883 | 2 |
| #31770644 | 2 |
| #31770627 | 2 |
| #31770603 | 2 |
| #476×C269 | 2 |
| #3079 | 269 |