Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31771258 | C2 | semidirect |
| 2. #31771240 | C2 | semidirect |
| 3. #31770917 | C2 | semidirect |
| 4. #31770882 | C2 | semidirect |
| 5. #31770840 | C2 | semidirect |
| 6. #31770797 | C2 | semidirect |
| 7. #31770740 | C2 | semidirect |
| 8. C4×D2152 | C2 | semidirect |
| 9. C8×D1076 | C2 | semidirect |
| 10. #102×D269 | C2 | semidirect |
| 11. #486×C269 | C2 | semidirect |
| 16. C2×#16864387 | C22 | semidirect |
| 17. C2×C8×D269 | C22 | semidirect |
| 20. #22575428 | C22 | semidirect |
| 26. C4×D1076 | C22 | semidirect |
| 27. C4⋊C4×D269 | C22 | semidirect |
| 28. #22575387 | C22 | semidirect |
| 29. #22575386 | C22 | semidirect |
| 30. C4⋊#14524130 | C22 | semidirect |
| 32. #22575375 | C22 | semidirect |
| 33. #22575374 | C22 | semidirect |
| 35. #22575365 | C22 | semidirect |
| 36. C4⋊Q8×C269 | C22 | semidirect |
| 38. #102×C269 | C22 | semidirect |
| 39. #102×C269 | C22 | semidirect |
| 40. C4×C8×C269 | C22 | semidirect |
| 88. D1076 | D8 | semidirect |
| 89. D1076 | #41 | semidirect |
| 142. C269 | #3294 | semidirect |
| 146. #486 | D269 | semidirect |
| 161. C4⋊Q8 | C2×D269 | semidirect |
| 180. #102 | C2×D269 | semidirect |
| 181. #102 | C2×D269 | semidirect |
| 183. C4×C8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771258 | 2 |
| #31771240 | 2 |
| #31770917 | 2 |
| #31770882 | 2 |
| #31770840 | 2 |
| #31770797 | 2 |
| #31770740 | 2 |
| C4×D2152 | 2 |
| C8×D1076 | 2 |
| #102×D269 | 2 |
| #486×C269 | 2 |
| #3294 | 269 |