Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
941 conjugacy classes of subgroups.
The subgroup lattice has 641 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10589171 | C2 | direct (N × H) |
| 22. C2×C3×#208 | C4 | semidirect |
| 23. C2×C3×#208 | C4 | semidirect |
| 24. C2×C3×#208 | C4 | semidirect |
| 28. C22×C3×C3⋊C8 | C4 | semidirect |
| 67. C3×#208 | C2×C4 | semidirect |
| 73. C2×C3×C3⋊C8 | C2×C4 | semidirect |
| 120. C2×#208 | Dic3 | semidirect |
| 121. C2×#208 | Dic3 | semidirect |
| 122. C2×#208 | Dic3 | semidirect |
| 126. C22×C3⋊C8 | Dic3 | semidirect |
| 258. #208 | C2×Dic3 | semidirect |
| 264. C2×C3⋊C8 | C2×Dic3 | semidirect |
| 434. C2×C32 | #344 | semidirect |
| 541. C32 | C2×#344 | semidirect |
| 602. C2×C3 | #4556 | semidirect |
| 603. C2×C3 | #4559 | semidirect |
| 630. C3 | C2×#4556 | semidirect |
| 631. C3 | C2×#4559 | semidirect |
| 638. C2 | #10589171 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64135 | 2 |
| C22×C3×#208 | 2 |
| #10589171 | 2 |
| C2×#4559 | 3 |
| C2×#4556 | 3 |