Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 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. C2×#22575481 | C2 | semidirect |
| 2. #31771155 | C2 | semidirect |
| 3. C2×C4×D1076 | C2 | semidirect |
| 4. #31770821 | C2 | semidirect |
| 5. #31770811 | C2 | semidirect |
| 6. #31770801 | C2 | semidirect |
| 7. #31770607 | C2 | semidirect |
| 8. #423×C269 | C2 | semidirect |
| 15. #22575453 | C22 | semidirect |
| 16. #22575450 | C22 | semidirect |
| 17. #22575441 | C22 | semidirect |
| 28. #22575378 | C22 | semidirect |
| 29. #22575375 | C22 | semidirect |
| 32. C4⋊C8×C269 | C22 | semidirect |
| 33. C4⋊C8×C269 | C22 | semidirect |
| 42. C2×D1076 | D4 | semidirect |
| 118. C4×C269 | AGL(1,ℤ/8) | semidirect |
| 129. C269 | #3036 | semidirect |
| 137. #423 | D269 | semidirect |
| 160. C4⋊C8 | C2×D269 | semidirect |
| 161. C4⋊C8 | C2×D269 | semidirect |
| 250. C4 | #22575481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575481 | 2 |
| #31771155 | 2 |
| C2×C4×D1076 | 2 |
| #31770821 | 2 |
| #31770811 | 2 |
| #31770801 | 2 |
| #31770607 | 2 |
| #423×C269 | 2 |
| #3036 | 269 |