Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1249 conjugacy classes of subgroups.
The subgroup lattice has 429 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. #71569 | C3 | direct (N × H) |
| 13. C2×C32×C4⋊C4 | C4 | semidirect |
| 65. C2×C3×C4⋊C4 | Dic3 | semidirect |
| 66. C2×C3×C4⋊C4 | C3×C4 | semidirect |
| 183. C2×C4⋊C4 | C3×Dic3 | semidirect |
| 345. C32 | #1445 | semidirect |
| 418. C3 | #71569 | direct (N × H) |
| 419. C3 | C3×#1445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C4⋊C4 | 2 |
| C2×C3×C3⋊#95 | 2 |
| C3×#1445 | 3 |
| #71569 | 3 |