Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #31771162 | C2 | semidirect |
| 3. #31770906 | C2 | semidirect |
| 4. #31770896 | C2 | semidirect |
| 5. #31770886 | C2 | semidirect |
| 6. #31770647 | C2 | semidirect |
| 8. #423×C269 | C2 | semidirect |
| 11. #22575453 | C22 | semidirect |
| 12. #22575453 | C22 | semidirect |
| 13. #22575445 | C22 | semidirect |
| 25. #22575387 | C22 | semidirect |
| 26. #22575385 | C22 | semidirect |
| 31. C4⋊C8×C269 | C22 | semidirect |
| 32. C4⋊C8×C269 | C22 | semidirect |
| 38. C2×D1076 | Q8 | semidirect |
| 115. C269 | #3077 | semidirect |
| 123. #423 | D269 | semidirect |
| 145. C4⋊C8 | C2×D269 | semidirect |
| 146. C4⋊C8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771162 | 2 |
| C2×C4×D1076 | 2 |
| #31770906 | 2 |
| #31770896 | 2 |
| #31770886 | 2 |
| #31770647 | 2 |
| #31770611 | 2 |
| #423×C269 | 2 |
| #3077 | 269 |