Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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. #31770897 | C2 | semidirect |
| 3. #31770892 | C2 | semidirect |
| 4. #31770887 | C2 | semidirect |
| 5. #31770882 | C2 | semidirect |
| 6. #31770645 | C2 | semidirect |
| 7. #31770629 | C2 | semidirect |
| 9. C2×C4⋊Q8×C269 | C2 | semidirect |
| 36. #16864402 | Q8 | semidirect |
| 72. Dic538 | C2×Q8 | semidirect |
| 74. D1076 | C2×Q8 | semidirect |
| 121. C269 | #3079 | semidirect |
| 123. C2×C4⋊Q8 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16864402 | 2 |
| #31770897 | 2 |
| #31770892 | 2 |
| #31770887 | 2 |
| #31770882 | 2 |
| #31770645 | 2 |
| #31770629 | 2 |
| #31770604 | 2 |
| C2×C4⋊Q8×C269 | 2 |
| #3079 | 269 |