Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1929 conjugacy classes of subgroups.
The subgroup lattice has 424 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10591107 | C2 | direct (N × H) |
| 5. C2×#63567 | C2 | semidirect |
| 13. C22×#634 | C4 | semidirect |
| 24. #63567 | C22 | semidirect |
| 53. C2×#634 | C2×C4 | semidirect |
| 303. C2×C32 | #419 | semidirect |
| 368. C32 | C2×#419 | semidirect |
| 398. C2×C3 | #5004 | semidirect |
| 399. C2×C3 | #5120 | semidirect |
| 417. C3 | C2×#5004 | semidirect |
| 418. C3 | C2×#5120 | semidirect |
| 420. C2 | #10591107 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#634 | 2 |
| C2×C3×#926 | 2 |
| C22×C3×#208 | 2 |
| #10591107 | 2 |
| C2×#63567 | 2 |
| C2×#5120 | 3 |
| C2×#5004 | 3 |