Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
3550 conjugacy classes of subgroups.
The subgroup lattice has 276 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25×C103 | C23 |
| commutator | C23 | C23×C4×C103 |
| Frattini, cosocle | C24 | C24×C103 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C103×#1444 | C2 | direct (N × H) |
| 12. C2×#95×C103 | C4 | semidirect |
| 36. #95×C103 | C2×C4 | semidirect |
| 65. C22×C4×C103 | C4⋊C4 | semidirect |
| 106. C2×C4×C103 | C2×C4⋊C4 | semidirect |
| 129. C2×#1444 | C103 | direct (N × H) |
| 130. C2×C103 | #1444 | direct (N × H) |
| 141. #1444 | C2×C103 | direct (N × H) |
| 142. C103 | C2×#1444 | direct (N × H) |
| 150. C2×#95 | C4×C103 | semidirect |
| 174. #95 | C2×C4×C103 | semidirect |
| 203. C22×C4 | C4⋊C4×C103 | semidirect |
| 244. C2×C4 | C2×C4⋊C4×C103 | semidirect |
| 267. C2 | C103×#1444 | 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×C103 | 2 |
| C22×#95×C103 | 2 |
| C103×#1444 | 2 |
| C2×#1444 | 103 |