Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
488 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 119 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. #31771150 | C2 | semidirect |
| 2. C2×#22575415 | C2 | semidirect |
| 3. #31770923 | C2 | semidirect |
| 4. #31770894 | C2 | semidirect |
| 5. #31770799 | C2 | semidirect |
| 6. #31770741 | C2 | semidirect |
| 7. #31770738 | C2 | semidirect |
| 8. #31770716 | C2 | semidirect |
| 9. #31770714 | C2 | semidirect |
| 10. #31770659 | C2 | semidirect |
| 11. #481×C269 | C2 | semidirect |
| 17. #22575452 | C22 | semidirect |
| 18. #22575449 | C22 | semidirect |
| 22. D4×Dic269 | C22 | semidirect |
| 27. #22575415 | C22 | semidirect |
| 31. #22575384 | C22 | semidirect |
| 32. #22575382 | C22 | semidirect |
| 35. #22575373 | C22 | semidirect |
| 37. #22575363 | C22 | semidirect |
| 40. #106×C269 | C22 | semidirect |
| 41. #102×C269 | C22 | semidirect |
| 92. D1076 | #41 | semidirect |
| 149. C269 | #3109 | semidirect |
| 154. #481 | D269 | semidirect |
| 184. #106 | C2×D269 | semidirect |
| 189. #102 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771150 | 2 |
| C2×#22575415 | 2 |
| #31770923 | 2 |
| #31770894 | 2 |
| #31770799 | 2 |
| #31770741 | 2 |
| #31770738 | 2 |
| #31770716 | 2 |
| #31770714 | 2 |
| #31770659 | 2 |
| #481×C269 | 2 |
| #3109 | 269 |