Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
2190 conjugacy classes of subgroups.
The subgroup lattice has 374 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C113 | C22⋊C4 |
| commutator | C22 | C22×C42×C113 |
| Frattini, cosocle | C22×C4 | C24×C113 |
| socle | C23×C113 | C2×C22⋊C4 |
| prime radical | C25×C113 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C113 ◁ C24×C4×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C113×#1742 | C2 | direct (N × H) |
| 4. C2×#343×C113 | C2 | semidirect |
| 9. C22×M16×C113 | C4 | semidirect |
| 21. #343×C113 | C22 | semidirect |
| 41. C2×M16×C113 | C2×C4 | semidirect |
| 179. C2×#1742 | C113 | direct (N × H) |
| 184. C2×C113 | #1742 | direct (N × H) |
| 189. #1742 | C2×C113 | direct (N × H) |
| 190. C2×#343 | C2×C113 | semidirect |
| 191. C113 | C2×#1742 | direct (N × H) |
| 196. C22×M16 | C4×C113 | semidirect |
| 208. #343 | C22×C113 | semidirect |
| 228. C2×M16 | C2×C4×C113 | semidirect |
| 370. C2 | C113×#1742 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×M16×C113 | 2 |
| C22×#117×C113 | 2 |
| C113×#1742 | 2 |
| C2×#343×C113 | 2 |
| C2×#1742 | 113 |