Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1560 conjugacy classes of subgroups.
The subgroup lattice has 384 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C32 | C23 |
| commutator | C23 | C22×C32×C4 |
| Frattini, cosocle | C24 | C23×C32 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C3×#1442 | C3 | direct (N × H) |
| 17. C32×#95 | C4 | semidirect |
| 54. #1442 | C32 | direct (N × H) |
| 65. C3×#95 | C3×C4 | semidirect |
| 180. #95 | C32×C4 | semidirect |
| 291. C32 | #1442 | direct (N × H) |
| 371. C3 | C3×#1442 | direct (N × H) |
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×C32×#95 | 2 |
| C3×#1442 | 3 |