Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×Q8×D269 | C2 | semidirect |
| 2. C2×#22575485 | C2 | semidirect |
| 4. #31770760 | C2 | semidirect |
| 5. #31770759 | C2 | semidirect |
| 6. #31770746 | C2 | semidirect |
| 7. #31770745 | C2 | semidirect |
| 8. #31770744 | C2 | semidirect |
| 9. #31770612 | C2 | semidirect |
| 10. #31770567 | C2 | semidirect |
| 11. #451×C269 | C2 | semidirect |
| 23. C2×#16864392 | C22 | semidirect |
| 24. C2×#16864391 | C22 | semidirect |
| 25. C2×#16864389 | C22 | semidirect |
| 35. #22575378 | C22 | semidirect |
| 36. #22575377 | C22 | semidirect |
| 37. #22575376 | C22 | semidirect |
| 41. C2×Q16×C269 | C22 | semidirect |
| 43. #103×C269 | C22 | semidirect |
| 58. Q8×D269 | D4 | semidirect |
| 141. C22×C269 | #137 | semidirect |
| 152. C2×D269 | #137 | semidirect |
| 169. C269 | #3004 | semidirect |
| 176. #451 | D269 | semidirect |
| 195. C2×Q16 | C2×D269 | semidirect |
| 211. #103 | C2×D269 | semidirect |
| 321. C22 | #22575485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D269 | 2 |
| C2×#22575485 | 2 |
| #31771118 | 2 |
| #31770760 | 2 |
| #31770759 | 2 |
| #31770746 | 2 |
| #31770745 | 2 |
| #31770744 | 2 |
| #31770612 | 2 |
| #31770567 | 2 |
| #451×C269 | 2 |
| #3004 | 269 |