Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
323 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 323 conjugacy classes of subgroups — too many to draw. Only its 80 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. D3×#818 | C2 | semidirect |
| 3. #10589371 | C2 | semidirect |
| 4. C3×#4509 | C2 | semidirect |
| 5. C3×(C2×D3)⋊C16 | C2 | semidirect |
| 6. #10589141 | C2 | semidirect |
| 7. #10589115 | C2 | semidirect |
| 29. #4509 | D3 | semidirect |
| 30. (C2×D3)⋊C16 | D3 | semidirect |
| 254. C32 | #2233 | semidirect |
| 298. C3 | #69096 | semidirect |
| 299. C3 | #69200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590831 | 2 |
| D3×#818 | 2 |
| #10589371 | 2 |
| C3×#4509 | 2 |
| C3×(C2×D3)⋊C16 | 2 |
| #10589141 | 2 |
| #10589115 | 2 |
| #69200 | 3 |
| #69096 | 3 |