Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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×#16864402 | C2 | semidirect |
| 2. C2×#22575481 | C2 | semidirect |
| 3. C2×#22575427 | C2 | semidirect |
| 4. #31770752 | C2 | semidirect |
| 5. #31770746 | C2 | semidirect |
| 6. #31770741 | C2 | semidirect |
| 7. #31770607 | C2 | semidirect |
| 8. #407×C269 | C2 | semidirect |
| 13. C2×#16864402 | C22 | semidirect |
| 14. C22×Dic538 | C22 | semidirect |
| 15. C22×D1076 | C22 | semidirect |
| 16. C22×D1076 | C22 | semidirect |
| 21. C2×#16864391 | C22 | semidirect |
| 22. C2×D2152 | C22 | semidirect |
| 26. #22575427 | C22 | semidirect |
| 27. C2×C4⋊Dic269 | C22 | semidirect |
| 29. #22575378 | C22 | semidirect |
| 30. #22575375 | C22 | semidirect |
| 32. C2×M16×C269 | C22 | semidirect |
| 33. C22⋊C8×C269 | C22 | semidirect |
| 34. C22⋊C8×C269 | C22 | semidirect |
| 42. #16864402 | D4 | semidirect |
| 89. Dic538 | C2×D4 | semidirect |
| 94. D1076 | C2×D4 | semidirect |
| 131. C22×C269 | AGL(1,ℤ/8) | semidirect |
| 155. C269 | #3006 | semidirect |
| 164. #407 | D269 | semidirect |
| 180. C2×M16 | C2×D269 | semidirect |
| 189. C22⋊C8 | C2×D269 | semidirect |
| 190. C22⋊C8 | C2×D269 | semidirect |
| 295. C22 | #22575481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864402 | 2 |
| C2×#22575481 | 2 |
| C2×#22575427 | 2 |
| #31770752 | 2 |
| #31770746 | 2 |
| #31770741 | 2 |
| #31770607 | 2 |
| #407×C269 | 2 |
| #3006 | 269 |