Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
2810 conjugacy classes of subgroups.
The subgroup lattice has 298 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22596908 | C2 | direct (N × H) |
| 3. C2×#17986026 | C2 | semidirect |
| 4. C2×#17986023 | C2 | semidirect |
| 5. C22×C4⋊(C71⋊C8) | C2 | semidirect |
| 11. #17986026 | C22 | semidirect |
| 12. #17986023 | C22 | semidirect |
| 17. C2×C4⋊(C71⋊C8) | C22 | semidirect |
| 113. C2×C4×C71 | #131 | semidirect |
| 140. C4×C71 | C2×#131 | semidirect |
| 145. C2×C71 | #2906 | semidirect |
| 155. C71 | C2×#2906 | semidirect |
| 262. C2×C4 | #14556135 | semidirect |
| 289. C4 | C2×#14556135 | semidirect |
| 293. C2 | #22596908 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556135 | 2 |
| #22596908 | 2 |
| C2×#17986026 | 2 |
| C2×#17986023 | 2 |
| C22×C4⋊(C71⋊C8) | 2 |
| C2×C4×#41×C71 | 2 |
| C2×#2906 | 71 |