Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3696 conjugacy classes of subgroups.
The subgroup lattice has 282 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C22×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 4. #10592911 | C2 | direct (N × H) |
| 5. C2×#63658 | C2 | semidirect |
| 9. C23×C32×C4 | C4 | semidirect |
| 17. C2×C4⋊(C3⋊Dic3) | C22 | semidirect |
| 18. #63658 | C22 | semidirect |
| 36. C22×C32×C4 | C2×C4 | semidirect |
| 49. C23×C3×C4 | Dic3 | semidirect |
| 65. C23×C32 | C4⋊C4 | semidirect |
| 78. C2×C32×C4 | C22⋊C4 | semidirect |
| 103. C22×C3×C4 | C2×Dic3 | semidirect |
| 120. C22×C32 | C2×C4⋊C4 | semidirect |
| 130. C32×C4 | C2×C22⋊C4 | semidirect |
| 135. C23×C4 | C3⋊Dic3 | semidirect |
| 150. C23×C3 | C4⋊Dic3 | semidirect |
| 163. C2×C3×C4 | #217 | semidirect |
| 172. C2×C32 | #380 | semidirect |
| 194. C22×C4 | C2×C3⋊Dic3 | semidirect |
| 207. C22×C3 | C2×C4⋊Dic3 | semidirect |
| 217. C3×C4 | C2×#217 | semidirect |
| 219. C32 | C2×#380 | semidirect |
| 226. C23 | C4⋊(C3⋊Dic3) | semidirect |
| 243. C2×C4 | #3757 | semidirect |
| 248. C2×C3 | #5212 | semidirect |
| 261. C22 | C2×C4⋊(C3⋊Dic3) | semidirect |
| 272. C4 | C2×#3757 | semidirect |
| 273. C3 | C2×#5212 | semidirect |
| 275. C2 | #10592911 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C32×C4 | 2 |
| C22×#3757 | 2 |
| C22×C4⋊(C3⋊Dic3) | 2 |
| #10592911 | 2 |
| C2×#63658 | 2 |
| C2×#5212 | 3 |