Finite Group DatabasebetaFinite Group DatabasebetaOrder 16384.
19665 conjugacy classes of subgroups.
The subgroup lattice has 462 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C4×C64 | C24 |
| socle, prime radical | C24 | C22×C4×C64 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C22×C4×C64 ▷ C2×C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. C4×C8×C128 | C4 | direct (N × H) |
| 30. C42×C128 | C8 | direct (N × H) |
| 67. C8×C128 | C42 | direct (N × H) |
| 118. C4×C128 | C4×C8 | direct (N × H) |
| 235. C42×C8 | C128 | direct (N × H) |
| 268. C128 | C42×C8 | direct (N × H) |
| 379. C4×C8 | C4×C128 | direct (N × H) |
| 417. C42 | C8×C128 | direct (N × H) |
| 443. C8 | C42×C128 | direct (N × H) |
| 453. C4 | C4×C8×C128 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C8×C64 | 2 |
| C43×C128 | 2 |
| C2×C4×C8×C128 | 2 |