Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
713 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 713 conjugacy classes of subgroups — too many to draw. Only its 196 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. C22×C3×C3⋊C16 | C2 | semidirect |
| 3. #10589108 | C2 | direct (N × H) |
| 12. C2×C3×C3⋊C16 | C22 | semidirect |
| 16. C22×C3⋊C16 | D3 | semidirect |
| 50. C2×C3⋊C16 | C2×D3 | semidirect |
| 54. C22×C3⋊D3 | C16 | semidirect |
| 110. C2×C3⋊D3 | C2×C16 | semidirect |
| 158. C2×C32 | C22⋊C16 | semidirect |
| 202. C32 | C2×C22⋊C16 | semidirect |
| 224. C2×C3 | (C2×D3)⋊C16 | semidirect |
| 243. C3 | C2×(C2×D3)⋊C16 | semidirect |
| 245. C2 | #10589108 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×C3⋊D3 | 2 |
| C22×C3×C3⋊C16 | 2 |
| #10589108 | 2 |
| C2×(C2×D3)⋊C16 | 3 |