Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
3070 conjugacy classes of subgroups.
The subgroup lattice has 300 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C113 | C23 |
| commutator | C22 | C22×C42×C113 |
| Frattini, cosocle | C24 | C24×C113 |
| socle | C24×C113 | C24 |
| prime radical | C25×C113 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C113×C4⋊#95 | C2 | semidirect |
| 5. C4×#95×C113 | C2 | semidirect |
| 10. C2×#117×C113 | C4 | semidirect |
| 14. C22×C42×C113 | C4 | semidirect |
| 35. C2×C4⋊C4×C113 | C2×C4 | semidirect |
| 46. C2×C42×C113 | C2×C4 | semidirect |
| 110. C2×C4×C113 | #95 | semidirect |
| 121. C2×C4×C113 | #117 | semidirect |
| 142. #13756 | C113 | direct (N × H) |
| 152. C4⋊#95 | C2×C113 | semidirect |
| 154. C4×#95 | C2×C113 | semidirect |
| 155. C113 | #13756 | direct (N × H) |
| 160. C2×#117 | C4×C113 | semidirect |
| 164. C22×C42 | C4×C113 | semidirect |
| 185. C2×C4⋊C4 | C2×C4×C113 | semidirect |
| 196. C2×C42 | C2×C4×C113 | semidirect |
| 260. C2×C4 | #95×C113 | semidirect |
| 271. C2×C4 | #117×C113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#117×C113 | 2 |
| C23×C42×C113 | 2 |
| C113×C4⋊#95 | 2 |
| C113×C22⋊#95 | 2 |
| C4×#95×C113 | 2 |
| #13756 | 113 |