Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
3854 conjugacy classes of subgroups.
The subgroup lattice has 328 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #22586570 | C2 | direct (N × H) |
| 8. C22×C4⋊Dic71 | C4 | semidirect |
| 15. C22×C42×C71 | C4 | semidirect |
| 26. C2×C4⋊Dic71 | C2×C4 | semidirect |
| 43. C2×C42×C71 | C2×C4 | semidirect |
| 75. C22×C4×C71 | C4⋊C4 | semidirect |
| 114. C2×C4×C71 | #95 | semidirect |
| 120. C2×C4×C71 | C2×C4⋊C4 | semidirect |
| 152. C4×C71 | C2×#95 | semidirect |
| 155. C2×C71 | C4⋊#95 | semidirect |
| 168. C71 | C2×C4⋊#95 | semidirect |
| 177. C22×C42 | Dic71 | semidirect |
| 206. C2×C42 | C2×Dic71 | semidirect |
| 238. C22×C4 | C4⋊Dic71 | semidirect |
| 284. C2×C4 | C71⋊#95 | semidirect |
| 290. C2×C4 | C2×C4⋊Dic71 | semidirect |
| 317. C4 | C2×C71⋊#95 | semidirect |
| 318. C2 | #22586570 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊Dic71 | 2 |
| C22×C71⋊#95 | 2 |
| #22586570 | 2 |
| C23×C42×C71 | 2 |
| C2×C4⋊#95 | 71 |