Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 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 |
|---|---|---|
| 1. #31771315 | C2 | semidirect |
| 3. #31770952 | C2 | semidirect |
| 4. #31770925 | C2 | semidirect |
| 5. #31770895 | C2 | semidirect |
| 6. #31770837 | C2 | semidirect |
| 7. #31770805 | C2 | semidirect |
| 8. #31770754 | C2 | semidirect |
| 9. C8×D1076 | C2 | semidirect |
| 10. #102×D269 | C2 | semidirect |
| 11. C4×SD16×C269 | C2 | semidirect |
| 14. C2×#16864389 | C22 | semidirect |
| 15. C2×C8×D269 | C22 | semidirect |
| 16. #22575453 | C22 | semidirect |
| 20. #22575429 | C22 | semidirect |
| 26. C4⋊C4×D269 | C22 | semidirect |
| 27. #22575384 | C22 | semidirect |
| 28. C4⋊#14524130 | C22 | semidirect |
| 29. #22575375 | C22 | semidirect |
| 30. #22575375 | C22 | semidirect |
| 32. #22575373 | C22 | semidirect |
| 33. #22575365 | C22 | semidirect |
| 35. C4×Q8×C269 | C22 | semidirect |
| 37. #106×C269 | C22 | semidirect |
| 38. #103×C269 | C22 | semidirect |
| 40. C4×C8×C269 | C22 | semidirect |
| 88. D1076 | SD16 | semidirect |
| 136. C269 | #3295 | semidirect |
| 146. C4×SD16 | D269 | semidirect |
| 162. C4×Q8 | C2×D269 | semidirect |
| 168. #106 | C2×D269 | semidirect |
| 170. #103 | C2×D269 | semidirect |
| 177. C4×C8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771315 | 2 |
| D4×D1076 | 2 |
| #31770952 | 2 |
| #31770925 | 2 |
| #31770895 | 2 |
| #31770837 | 2 |
| #31770805 | 2 |
| #31770754 | 2 |
| C8×D1076 | 2 |
| #102×D269 | 2 |
| C4×SD16×C269 | 2 |
| #3295 | 269 |