Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1193 conjugacy classes of subgroups.
The subgroup lattice has 266 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10591138 | C2 | direct (N × H) |
| 4. C2×#63576 | C2 | semidirect |
| 5. C2×#63574 | C2 | semidirect |
| 8. C22×C3⋊(C3⋊C8) | C4 | semidirect |
| 17. #63576 | C22 | semidirect |
| 18. #63574 | C22 | semidirect |
| 36. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 180. C2×C32 | #427 | semidirect |
| 222. C32 | C2×#427 | semidirect |
| 245. C2×C3 | #4998 | semidirect |
| 260. C3 | C2×#4998 | semidirect |
| 262. C2 | #10591138 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3⋊(C3⋊C8) | 2 |
| C2×C3×#926 | 2 |
| #10591138 | 2 |
| C2×#63576 | 2 |
| C2×#63574 | 2 |
| C2×#4998 | 3 |