Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
2122 conjugacy classes of subgroups.
The subgroup lattice has 360 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22597006 | C2 | semidirect |
| 2. #22596978 | C2 | semidirect |
| 3. #22596973 | C2 | semidirect |
| 4. C2×#17986023 | C2 | semidirect |
| 6. #22596759 | C2 | semidirect |
| 9. #17986060 | C22 | semidirect |
| 10. #17986056 | C22 | semidirect |
| 11. #17986052 | C22 | semidirect |
| 14. #17986023 | C22 | semidirect |
| 15. C2×C4⋊(C71⋊C8) | C22 | semidirect |
| 18. #17985955 | C22 | semidirect |
| 187. C71 | #60125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597006 | 2 |
| #22596978 | 2 |
| #22596973 | 2 |
| C2×#17986023 | 2 |
| #22596785 | 2 |
| #22596759 | 2 |
| C2×C4×#41×C71 | 2 |
| #60125 | 71 |