Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
522 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 173 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×C16×C3⋊D3 | C2 | semidirect |
| 3. C32×C4×C16 | C2 | semidirect |
| 4. #10589373 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 18. C3×C4×C16 | D3 | semidirect |
| 32. C32×C16 | D4 | semidirect |
| 49. C4⋊(C3⋊D3) | C16 | direct (N × H) |
| 60. C4×C16 | C3⋊D3 | semidirect |
| 72. C3×C16 | D12 | semidirect |
| 77. C2×C3⋊D3 | C2×C16 | semidirect |
| 79. C32×C4 | C2×C16 | semidirect |
| 120. C16 | C4⋊(C3⋊D3) | direct (N × H) |
| 126. C3×C4 | D3×C16 | semidirect |
| 130. C32 | D4×C16 | semidirect |
| 153. C4 | C16×C3⋊D3 | semidirect |
| 156. C3 | C16×D12 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×C3⋊D3 | 2 |
| C8×C4⋊(C3⋊D3) | 2 |
| C32×C4×C16 | 2 |
| #10589373 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| C16×D12 | 3 |