Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
4894 conjugacy classes of subgroups.
The subgroup lattice has 306 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25×C109 | C23 |
| commutator | C22 | C24×C4×C109 |
| Frattini, cosocle | C23 | C25×C109 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C25×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C2×#389×C109 | C2 | direct (N × H) |
| 14. C22×C4⋊C4×C109 | C4 | semidirect |
| 20. #389×C109 | C22 | direct (N × H) |
| 45. C2×C4⋊C4×C109 | C2×C4 | semidirect |
| 73. C22×C4×C109 | C4⋊C4 | semidirect |
| 87. C4⋊C4×C109 | C22×C4 | semidirect |
| 117. C2×C4×C109 | C2×C4⋊C4 | semidirect |
| 124. C22×C109 | #389 | direct (N × H) |
| 143. C4×C109 | C22×C4⋊C4 | semidirect |
| 144. C22×#389 | C109 | direct (N × H) |
| 145. C2×C109 | C2×#389 | direct (N × H) |
| 157. C2×#389 | C2×C109 | direct (N × H) |
| 159. C109 | C22×#389 | direct (N × H) |
| 167. C22×C4⋊C4 | C4×C109 | semidirect |
| 173. #389 | C22×C109 | direct (N × H) |
| 198. C2×C4⋊C4 | C2×C4×C109 | semidirect |
| 226. C22×C4 | C4⋊C4×C109 | semidirect |
| 240. C4⋊C4 | C22×C4×C109 | semidirect |
| 270. C2×C4 | C2×C4⋊C4×C109 | semidirect |
| 277. C22 | #389×C109 | direct (N × H) |
| 296. C4 | C22×C4⋊C4×C109 | semidirect |
| 297. C2 | C2×#389×C109 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊C4×C109 | 2 |
| C23×C42×C109 | 2 |
| C2×#389×C109 | 2 |
| C22×#95×C109 | 2 |
| C22×#389 | 109 |