Finite Group DatabasebetaFinite Group DatabasebetaOrder 24576.
366876 conjugacy classes of subgroups.
The subgroup lattice has 300 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C24×C16 | C25×C3 |
| socle, prime radical | C25×C3 | C24×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C44×C32 | C3 | direct (N × H) |
| 8. C3×C43×C32 | C4 | direct (N × H) |
| 24. C43×C32 | C3×C4 | direct (N × H) |
| 39. C3×C42×C32 | C42 | direct (N × H) |
| 63. C3×C44 | C32 | direct (N × H) |
| 83. C42×C32 | C3×C42 | direct (N × H) |
| 106. C3×C4×C32 | C43 | direct (N × H) |
| 121. C44 | C3×C32 | direct (N × H) |
| 144. C3×C43 | C4×C32 | direct (N × H) |
| 172. C4×C32 | C3×C43 | direct (N × H) |
| 192. C3×C32 | C44 | direct (N × H) |
| 210. C43 | C3×C4×C32 | direct (N × H) |
| 226. C3×C42 | C42×C32 | direct (N × H) |
| 250. C32 | C3×C44 | direct (N × H) |
| 270. C42 | C3×C42×C32 | direct (N × H) |
| 277. C3×C4 | C43×C32 | direct (N × H) |
| 293. C4 | C3×C43×C32 | direct (N × H) |
| 296. C3 | C44×C32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C44×C16 | 2 |
| C2×C3×C43×C32 | 2 |
| C44×C32 | 3 |