Finite Group DatabasebetaFinite Group DatabasebetaOrder 20736.
1395 conjugacy classes of subgroups.
The subgroup lattice has 195 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C8×C27 | C23×C3 |
| socle, prime radical | C23×C3 | C22×C8×C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C4×C16×C81 | C4 | direct (N × H) |
| 29. C42×C81 | C16 | direct (N × H) |
| 32. C16×C81 | C42 | direct (N × H) |
| 68. C4×C81 | C4×C16 | direct (N × H) |
| 78. C42×C16 | C81 | direct (N × H) |
| 116. C81 | C42×C16 | direct (N × H) |
| 128. C4×C16 | C4×C81 | direct (N × H) |
| 167. C42 | C16×C81 | direct (N × H) |
| 170. C16 | C42×C81 | direct (N × H) |
| 188. C4 | C4×C16×C81 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C8×C81 | 2 |
| C2×C4×C16×C81 | 2 |
| C42×C16×C27 | 3 |