Order 26368.
4622 conjugacy classes of subgroups.
The subgroup lattice has 340 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C103 | C23 |
| commutator | C23 | C23×C4×C103 |
| Frattini, cosocle | C24 | C24×C103 |
| prime radical | C26×C103 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C22×#95×C103 | C2 | semidirect |
| 4. C103×#1440 | C2 | direct (N × H) |
| 11. C22×C22⋊C4×C103 | C4 | semidirect |
| 15. C2×#95×C103 | C22 | semidirect |
| 42. C2×C22⋊C4×C103 | C2×C4 | semidirect |
| 162. C2×#1440 | C103 | direct (N × H) |
| 164. C2×C103 | #1440 | direct (N × H) |
| 172. C22×#95 | C2×C103 | semidirect |
| 173. #1440 | C2×C103 | direct (N × H) |
| 174. C103 | C2×#1440 | direct (N × H) |
| 181. C22×C22⋊C4 | C4×C103 | semidirect |
| 185. C2×#95 | C22×C103 | semidirect |
| 212. C2×C22⋊C4 | C2×C4×C103 | semidirect |
| 333. C2 | C103×#1440 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊C4×C103 | 2 |
| C22×#95×C103 | 2 |
| C103×#1440 | 2 |
| C2×#1440 | 103 |