Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2772 conjugacy classes of subgroups; only the 709 normal subgroups are shown.
This group has 2772 conjugacy classes of subgroups — too many to draw. Only its 709 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 |
|---|---|---|
| 2. C2×D4×C3⋊Dic3 | C2 | semidirect |
| 3. #10592920 | C2 | semidirect |
| 4. #10592634 | C2 | semidirect |
| 5. C42×C3⋊Dic3 | C2 | semidirect |
| 9. C32×#127 | C4 | semidirect |
| 24. C2×C32×D4 | C2×C4 | semidirect |
| 30. C32×C42 | C2×C4 | semidirect |
| 34. C4×C3⋊Dic3 | D4 | semidirect |
| 38. C3×#127 | Dic3 | semidirect |
| 66. C2×C3×D4 | C2×Dic3 | semidirect |
| 72. C3×C42 | C2×Dic3 | semidirect |
| 83. C32×C4 | C4×D4 | semidirect |
| 86. C3⋊Dic3 | #127 | direct (N × H) |
| 89. #127 | C3⋊Dic3 | direct (N × H) |
| 116. C2×D4 | C2×C3⋊Dic3 | semidirect |
| 126. C42 | C2×C3⋊Dic3 | semidirect |
| 133. C3×C4 | D4×Dic3 | semidirect |
| 137. C32 | C4×#127 | semidirect |
| 164. C4 | D4×C3⋊Dic3 | semidirect |
| 165. C3 | Dic3×#127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#127 | 2 |
| C2×D4×C3⋊Dic3 | 2 |
| #10592920 | 2 |
| #10592634 | 2 |
| C42×C3⋊Dic3 | 2 |
| Dic3×#127 | 3 |