Order 26368.
598 conjugacy classes of subgroups.
The subgroup lattice has 324 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C103 | C2×D4 |
| commutator | C2×C4 | C22×C8×C103 |
| Frattini, cosocle | C2×C42 | C23×C103 |
| socle | C23×C103 | C2×C4⋊C4 |
| prime radical | C24×C103 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C103 ◁ C22×C42×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#335×C103 | C2 | semidirect |
| 4. C103×#1277 | C2 | semidirect |
| 26. C22×C8×C103 | C8 | semidirect |
| 128. C8×C103 | C22⋊C8 | semidirect |
| 135. C22×C103 | #335 | semidirect |
| 153. #8596 | C103 | direct (N × H) |
| 164. C2×#335 | C2×C103 | semidirect |
| 165. #1277 | C2×C103 | semidirect |
| 166. C103 | #8596 | direct (N × H) |
| 188. C22×C8 | C8×C103 | semidirect |
| 290. C8 | C22⋊C8×C103 | semidirect |
| 297. C22 | #335×C103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C8×C103 | 2 |
| C103×#1797 | 2 |
| C2×#335×C103 | 2 |
| C103×#1277 | 2 |
| #8596 | 103 |