Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 137 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×#22575484 | C2 | semidirect |
| 3. #31771371 | C2 | semidirect |
| 4. #31770877 | C2 | semidirect |
| 5. #31770865 | C2 | semidirect |
| 6. #31770654 | C2 | semidirect |
| 7. #31770589 | C2 | semidirect |
| 8. C2×#22575372 | C2 | semidirect |
| 9. C2×#137×C269 | C2 | semidirect |
| 26. #22575389 | C22 | semidirect |
| 27. #22575372 | C22 | semidirect |
| 28. #22575372 | C22 | semidirect |
| 29. #22575370 | C22 | semidirect |
| 34. C2×Q16×C269 | C22 | semidirect |
| 35. C2×SD16×C269 | C22 | semidirect |
| 142. C269 | #3069 | semidirect |
| 146. C2×#137 | D269 | semidirect |
| 166. C2×Q16 | C2×D269 | semidirect |
| 168. C2×SD16 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771403 | 2 |
| C2×#22575484 | 2 |
| #31771371 | 2 |
| #31770877 | 2 |
| #31770865 | 2 |
| #31770654 | 2 |
| #31770589 | 2 |
| C2×#22575372 | 2 |
| C2×#137×C269 | 2 |
| #3069 | 269 |