Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
488 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 488 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×C4×D1084 | C2 | semidirect |
| 2. #31774213 | C2 | semidirect |
| 3. #31774184 | C2 | semidirect |
| 4. #31774089 | C2 | semidirect |
| 5. #31774030 | C2 | semidirect |
| 6. #31774007 | C2 | semidirect |
| 7. #31773954 | C2 | semidirect |
| 8. #532×C271 | C2 | semidirect |
| 18. #22576091 | C22 | semidirect |
| 19. C4⋊(C271⋊C8) | C22 | semidirect |
| 20. #22576081 | C22 | semidirect |
| 23. #22576071 | C22 | semidirect |
| 25. C4⋊Q8×C271 | C22 | semidirect |
| 26. #127×C271 | C22 | semidirect |
| 31. C4×D4×C271 | C22 | semidirect |
| 71. D1084 | #41 | semidirect |
| 120. C271 | #3109 | semidirect |
| 122. #532 | D271 | semidirect |
| 134. C4⋊Q8 | C2×D271 | semidirect |
| 135. #127 | C2×D271 | semidirect |
| 144. C4×D4 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1084 | 2 |
| #31774213 | 2 |
| #31774184 | 2 |
| #31774089 | 2 |
| #31774030 | 2 |
| #31774007 | 2 |
| #31773954 | 2 |
| #532×C271 | 2 |
| #3109 | 271 |