Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
488 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31771153 | C2 | semidirect |
| 2. C4×D4×D269 | C2 | semidirect |
| 3. #31770922 | C2 | semidirect |
| 4. #31770896 | C2 | semidirect |
| 5. #31770895 | C2 | semidirect |
| 6. #31770797 | C2 | semidirect |
| 7. #31770737 | C2 | semidirect |
| 8. #31770717 | C2 | semidirect |
| 9. #31770714 | C2 | semidirect |
| 10. #31770661 | C2 | semidirect |
| 11. #459×C269 | C2 | semidirect |
| 16. #22575453 | C22 | semidirect |
| 23. D4×Dic269 | C22 | semidirect |
| 30. #22575385 | C22 | semidirect |
| 31. #22575384 | C22 | semidirect |
| 32. C4⋊#14524130 | C22 | semidirect |
| 35. #22575374 | C22 | semidirect |
| 37. #22575363 | C22 | semidirect |
| 39. #127×C269 | C22 | semidirect |
| 41. C4⋊C8×C269 | C22 | semidirect |
| 42. #102×C269 | C22 | semidirect |
| 91. D1076 | #41 | semidirect |
| 116. D4×C269 | #41 | semidirect |
| 154. C269 | #3109 | semidirect |
| 162. #459 | D269 | semidirect |
| 173. #127 | C2×D269 | semidirect |
| 191. C4⋊C8 | C2×D269 | semidirect |
| 195. #102 | C2×D269 | semidirect |
| 256. D4 | #16864401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771153 | 2 |
| C4×D4×D269 | 2 |
| #31770922 | 2 |
| #31770896 | 2 |
| #31770895 | 2 |
| #31770797 | 2 |
| #31770737 | 2 |
| #31770717 | 2 |
| #31770714 | 2 |
| #31770661 | 2 |
| #459×C269 | 2 |
| #3109 | 269 |