Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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×#22575475 | C2 | semidirect |
| 2. #31771046 | C2 | semidirect |
| 3. #31771045 | C2 | semidirect |
| 4. #31771041 | C2 | semidirect |
| 5. #31771040 | C2 | semidirect |
| 6. #31771035 | C2 | semidirect |
| 7. C2×#22575393 | C2 | semidirect |
| 8. C2×#135×C269 | C2 | semidirect |
| 13. #22575475 | C22 | semidirect |
| 14. C2×Dic1076 | C22 | semidirect |
| 16. C2×D2152 | C22 | semidirect |
| 17. #22575399 | C22 | semidirect |
| 18. #22575397 | C22 | semidirect |
| 19. #22575396 | C22 | semidirect |
| 20. #22575394 | C22 | semidirect |
| 21. #22575393 | C22 | semidirect |
| 22. #22575393 | C22 | semidirect |
| 23. C2×#16864377 | C22 | semidirect |
| 28. #135×C269 | C22 | semidirect |
| 29. C2×Q16×C269 | C22 | semidirect |
| 31. C2×D8×C269 | C22 | semidirect |
| 120. C269 | #3414 | semidirect |
| 123. C2×#135 | D269 | semidirect |
| 139. #135 | C2×D269 | semidirect |
| 141. C2×Q16 | C2×D269 | semidirect |
| 145. C2×D8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575475 | 2 |
| #31771046 | 2 |
| #31771045 | 2 |
| #31771041 | 2 |
| #31771040 | 2 |
| #31771035 | 2 |
| C2×#22575393 | 2 |
| C2×#135×C269 | 2 |
| #3414 | 269 |