Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 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×#16864401 | C2 | semidirect |
| 3. #31770717 | C2 | semidirect |
| 4. #31770713 | C2 | semidirect |
| 5. #31770711 | C2 | semidirect |
| 6. #31770705 | C2 | semidirect |
| 7. #31770702 | C2 | semidirect |
| 8. #31770640 | C2 | semidirect |
| 9. #31770598 | C2 | semidirect |
| 10. #97×D269 | C2 | semidirect |
| 11. #442×C269 | C2 | semidirect |
| 13. #22575472 | C4 | semidirect |
| 41. #16864401 | C2×C4 | semidirect |
| 48. Dic1076 | C2×C4 | semidirect |
| 49. #16864390 | C2×C4 | semidirect |
| 53. C8×D269 | C2×C4 | semidirect |
| 66. D8×C269 | C2×C4 | semidirect |
| 114. C269 | #2943 | semidirect |
| 119. #442 | D269 | semidirect |
| 167. D8 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575472 | 2 |
| C4×#16864401 | 2 |
| #31770717 | 2 |
| #31770713 | 2 |
| #31770711 | 2 |
| #31770705 | 2 |
| #31770702 | 2 |
| #31770640 | 2 |
| #31770598 | 2 |
| #97×D269 | 2 |
| #442×C269 | 2 |
| #2943 | 269 |