Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
480 conjugacy classes of subgroups.
The subgroup lattice has 350 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17985781 | C2 | semidirect |
| 2. C2×C71⋊#338 | C2 | semidirect |
| 3. #22586331 | C2 | direct (N × H) |
| 8. #17985781 | C22 | semidirect |
| 10. C71⋊#338 | C22 | semidirect |
| 173. C2×C71 | #1341 | semidirect |
| 179. C71 | C2×#1341 | semidirect |
| 347. C2 | #22586331 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985781 | 2 |
| C2×C71⋊#338 | 2 |
| #22586331 | 2 |
| C2×#469×C71 | 2 |
| C2×#1341 | 71 |