Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2830 conjugacy classes of subgroups.
The subgroup lattice has 280 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C73 | C24 |
| commutator | C22 | C24×C4×C73 |
| Frattini, cosocle | C2×C4 | C25×C73 |
| socle | C23×C73 | C23×C4 |
| prime radical | C25×C73 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C73×#2905 | C2 | direct (N × H) |
| 4. C2×#424×C73 | C2 | semidirect |
| 5. C2×#423×C73 | C2 | semidirect |
| 19. #424×C73 | C22 | semidirect |
| 20. #423×C73 | C22 | semidirect |
| 21. C2×C4⋊C8×C73 | C22 | semidirect |
| 51. C4⋊C8×C73 | C23 | semidirect |
| 134. C2×#2905 | C73 | direct (N × H) |
| 137. C2×C73 | #2905 | direct (N × H) |
| 142. #2905 | C2×C73 | direct (N × H) |
| 143. C2×#424 | C2×C73 | semidirect |
| 144. C2×#423 | C2×C73 | semidirect |
| 145. C73 | C2×#2905 | direct (N × H) |
| 159. #424 | C22×C73 | semidirect |
| 160. #423 | C22×C73 | semidirect |
| 161. C2×C4⋊C8 | C22×C73 | semidirect |
| 191. C4⋊C8 | C23×C73 | semidirect |
| 276. C2 | C73×#2905 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×M16×C73 | 2 |
| C22×#117×C73 | 2 |
| C73×#2905 | 2 |
| C2×#424×C73 | 2 |
| C2×#423×C73 | 2 |
| C2×#2905 | 73 |