Finite Group DatabasebetaFinite Group DatabasebetaOrder 18432.
4632 conjugacy classes of subgroups.
The subgroup lattice has 558 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4×C32 | C24×C3 |
| socle, prime radical | C24×C3 | C3×C4×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C8×C9×C64 | C2 | direct (N × H) |
| 13. C8×C9×C64 | C22 | direct (N × H) |
| 31. C22×C9×C64 | C8 | direct (N × H) |
| 35. C22×C8×C64 | C9 | direct (N × H) |
| 47. C2×C8×C64 | C2×C9 | direct (N × H) |
| 66. C2×C9×C64 | C2×C8 | direct (N × H) |
| 127. C9×C64 | C22×C8 | direct (N × H) |
| 136. C8×C64 | C22×C9 | direct (N × H) |
| 167. C22×C8×C9 | C64 | direct (N × H) |
| 204. C22×C64 | C8×C9 | direct (N × H) |
| 261. C2×C8×C9 | C2×C64 | direct (N × H) |
| 297. C2×C64 | C2×C8×C9 | direct (N × H) |
| 355. C8×C9 | C22×C64 | direct (N × H) |
| 392. C64 | C22×C8×C9 | direct (N × H) |
| 421. C22×C9 | C8×C64 | direct (N × H) |
| 432. C22×C8 | C9×C64 | direct (N × H) |
| 482. C2×C9 | C2×C8×C64 | direct (N × H) |
| 495. C2×C8 | C2×C9×C64 | direct (N × H) |
| 522. C9 | C22×C8×C64 | direct (N × H) |
| 535. C8 | C22×C9×C64 | direct (N × H) |
| 544. C22 | C8×C9×C64 | direct (N × H) |
| 554. C2 | C2×C8×C9×C64 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×C9×C32 | 2 |
| C22×C4×C9×C64 | 2 |
| C2×C8×C9×C64 | 2 |
| C22×C3×C8×C64 | 3 |