Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2772 conjugacy classes of subgroups; only the 649 normal subgroups are shown.
This group has 2772 conjugacy classes of subgroups — too many to draw. Only its 649 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×C4×C4⋊(C3⋊D3) | C2 | semidirect |
| 3. C32×C43 | C2 | semidirect |
| 4. #10592638 | C2 | semidirect |
| 5. #10592634 | C2 | semidirect |
| 14. #64083 | C4 | direct (N × H) |
| 18. C3×C43 | D3 | semidirect |
| 28. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 31. C32×C42 | C2×C4 | semidirect |
| 32. C32×C42 | D4 | semidirect |
| 62. C43 | C3⋊D3 | semidirect |
| 73. C3×C42 | C4×D3 | semidirect |
| 74. C3×C42 | D12 | semidirect |
| 84. C32×C4 | C4×D4 | semidirect |
| 85. C32×C4 | #127 | semidirect |
| 125. C42 | C4×C3⋊D3 | semidirect |
| 126. C42 | C4⋊(C3⋊D3) | semidirect |
| 134. C3×C4 | C4×D12 | semidirect |
| 135. C3×C4 | #874 | semidirect |
| 137. C32 | C4×#127 | semidirect |
| 163. C4 | C4×C4⋊(C3⋊D3) | semidirect |
| 164. C4 | #64083 | direct (N × H) |
| 165. C3 | C4×#874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64083 | 2 |
| C2×C4×C4⋊(C3⋊D3) | 2 |
| C32×C43 | 2 |
| #10592638 | 2 |
| #10592634 | 2 |
| C4×#874 | 3 |