Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
330 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 123 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. C32×C4×C16 | C2 | semidirect |
| 3. C4⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 13. C3×C4×C16 | D3 | semidirect |
| 41. C4⋊(C3⋊D3) | C16 | semidirect |
| 50. C4×C16 | C3⋊D3 | semidirect |
| 119. C32 | D4⋊C16 | semidirect |
| 147. C3 | #67503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C4⋊(C3⋊D3) | 2 |
| C32×C4×C16 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #67503 | 3 |