Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #31770956 | C2 | semidirect |
| 4. #31770942 | C2 | semidirect |
| 5. #31770900 | C2 | semidirect |
| 6. #31770845 | C2 | semidirect |
| 7. #31770815 | C2 | semidirect |
| 8. #31770759 | C2 | semidirect |
| 10. #103×D269 | C2 | semidirect |
| 11. C4×Q16×C269 | C2 | semidirect |
| 81. D1076 | Q16 | semidirect |
| 122. C269 | #3299 | semidirect |
| 132. C4×Q16 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771315 | 2 |
| Q8×D1076 | 2 |
| #31770956 | 2 |
| #31770942 | 2 |
| #31770900 | 2 |
| #31770845 | 2 |
| #31770815 | 2 |
| #31770759 | 2 |
| C8×D1076 | 2 |
| #103×D269 | 2 |
| C4×Q16×C269 | 2 |
| #3299 | 269 |