Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
2830 conjugacy classes of subgroups.
The subgroup lattice has 280 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22596904 | C2 | direct (N × H) |
| 3. C2×#17986026 | C2 | semidirect |
| 4. C2×#17986023 | C2 | semidirect |
| 11. #17986026 | C22 | semidirect |
| 12. #17986023 | C22 | semidirect |
| 13. C2×C4⋊(C71⋊C8) | C22 | semidirect |
| 30. C4⋊(C71⋊C8) | C23 | semidirect |
| 137. C2×C71 | #2905 | semidirect |
| 145. C71 | C2×#2905 | semidirect |
| 276. C2 | #22596904 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11765849 | 2 |
| #22596904 | 2 |
| C2×#17986026 | 2 |
| C2×#17986023 | 2 |
| C22×#117×C71 | 2 |
| C2×#2905 | 71 |