Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 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×Dic86 | C2 | semidirect |
| 3. #13063302 | C2 | direct (N × H) |
| 4. C2×C4⋊Dic43 | C2 | semidirect |
| 5. C2×Dic43⋊C4 | C2 | semidirect |
| 6. C2×Dic43⋊C4 | C2 | semidirect |
| 19. C2×Dic86 | C22 | semidirect |
| 22. C4⋊Dic43 | C22 | semidirect |
| 23. Dic43⋊C4 | C22 | semidirect |
| 24. Dic43⋊C4 | C22 | semidirect |
| 27. C23×C43 | Q8 | semidirect |
| 49. C22×C43 | C2×Q8 | semidirect |
| 59. C2×C43 | C22⋊Q8 | semidirect |
| 64. C43 | C2×C22⋊Q8 | semidirect |
| 91. C23 | Dic86 | semidirect |
| 112. C22 | C2×Dic86 | semidirect |
| 123. C2 | #13063302 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic86 | 2 |
| C23×Dic43 | 2 |
| #13063302 | 2 |
| C2×C4⋊Dic43 | 2 |
| C2×Dic43⋊C4 | 2 |
| C2×C22⋊Dic43 | 2 |
| C2×C22⋊C4×C43 | 2 |
| C2×C22⋊Q8 | 43 |