Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. C22×#16864389 | C2 | semidirect |
| 3. #31771079 | C2 | semidirect |
| 4. #31770817 | C2 | semidirect |
| 5. #31770807 | C2 | semidirect |
| 6. #31770632 | C2 | semidirect |
| 7. #31770614 | C2 | semidirect |
| 8. #31770601 | C2 | semidirect |
| 9. #536×C269 | C2 | semidirect |
| 22. C4⋊#14524130 | C22 | semidirect |
| 23. #22575377 | C22 | semidirect |
| 24. #22575377 | C22 | semidirect |
| 25. #22575374 | C22 | semidirect |
| 28. C4⋊Q8×C269 | C22 | semidirect |
| 29. #124×C269 | C22 | semidirect |
| 116. C269 | #3042 | semidirect |
| 120. #536 | D269 | semidirect |
| 137. C4⋊Q8 | C2×D269 | semidirect |
| 138. #124 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575478 | 2 |
| C22×#16864389 | 2 |
| #31771079 | 2 |
| #31770817 | 2 |
| #31770807 | 2 |
| #31770632 | 2 |
| #31770614 | 2 |
| #31770601 | 2 |
| #536×C269 | 2 |
| #3042 | 269 |