Finite Group DatabasebetaFinite Group DatabasebetaOrder 28672.
6214 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 | C4×C8×C16 | C23×C7 |
| socle, prime radical | C23×C7 | C4×C8×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. C8×C16×C32 | C7 | direct (N × H) |
| 23. C7×C16×C32 | C8 | direct (N × H) |
| 48. C7×C8×C32 | C16 | direct (N × H) |
| 68. C7×C8×C16 | C32 | direct (N × H) |
| 85. C16×C32 | C7×C8 | direct (N × H) |
| 124. C8×C32 | C7×C16 | direct (N × H) |
| 149. C7×C32 | C8×C16 | direct (N × H) |
| 166. C8×C16 | C7×C32 | direct (N × H) |
| 188. C7×C16 | C8×C32 | direct (N × H) |
| 222. C7×C8 | C16×C32 | direct (N × H) |
| 247. C32 | C7×C8×C16 | direct (N × H) |
| 271. C16 | C7×C8×C32 | direct (N × H) |
| 284. C8 | C7×C16×C32 | direct (N × H) |
| 288. C7 | C8×C16×C32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C8×C162 | 2 |
| C7×C82×C32 | 2 |
| C4×C7×C16×C32 | 2 |
| C8×C16×C32 | 7 |