Finite Group DatabasebetaFinite Group DatabasebetaOrder 28672.
322294 conjugacy classes of subgroups.
The subgroup lattice has 146 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C32 | C27×C7 |
| socle, prime radical | C27×C7 | C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C25×C7×C64 | C2 | direct (N × H) |
| 6. C24×C7×C64 | C22 | direct (N × H) |
| 7. C26×C64 | C7 | direct (N × H) |
| 13. C23×C7×C64 | C23 | direct (N × H) |
| 15. C25×C64 | C2×C7 | direct (N × H) |
| 19. C24×C64 | C22×C7 | direct (N × H) |
| 27. C22×C7×C64 | C24 | direct (N × H) |
| 37. C2×C7×C64 | C25 | direct (N × H) |
| 43. C23×C64 | C23×C7 | direct (N × H) |
| 44. C26×C7 | C64 | direct (N × H) |
| 54. C7×C64 | C26 | direct (N × H) |
| 62. C22×C64 | C24×C7 | direct (N × H) |
| 63. C25×C7 | C2×C64 | direct (N × H) |
| 82. C2×C64 | C25×C7 | direct (N × H) |
| 83. C24×C7 | C22×C64 | direct (N × H) |
| 91. C26 | C7×C64 | direct (N × H) |
| 101. C64 | C26×C7 | direct (N × H) |
| 102. C23×C7 | C23×C64 | direct (N × H) |
| 108. C25 | C2×C7×C64 | direct (N × H) |
| 118. C22×C7 | C24×C64 | direct (N × H) |
| 122. C24 | C22×C7×C64 | direct (N × H) |
| 130. C2×C7 | C25×C64 | direct (N × H) |
| 132. C23 | C23×C7×C64 | direct (N × H) |
| 138. C7 | C26×C64 | direct (N × H) |
| 139. C22 | C24×C7×C64 | direct (N × H) |
| 143. C2 | C25×C7×C64 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C26×C7×C32 | 2 |
| C25×C7×C64 | 2 |
| C26×C64 | 7 |