Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
504 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22597396 | C2 | semidirect |
| 3. C2×#17985732 | C2 | semidirect |
| 4. #22586701 | C2 | semidirect |
| 5. #22586227 | C2 | semidirect |
| 6. #22586183 | C2 | semidirect |
| 7. C71×#1504 | C2 | semidirect |
| 9. #17986332 | C4 | semidirect |
| 11. #17986315 | C4 | semidirect |
| 14. #17986149 | C4 | semidirect |
| 16. #17986132 | C4 | semidirect |
| 248. #1504 | D71 | semidirect |
| 253. C71 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599101 | 2 |
| #22597396 | 2 |
| C2×#17985732 | 2 |
| #22586701 | 2 |
| #22586227 | 2 |
| #22586183 | 2 |
| C71×#1504 | 2 |
| #9264 | 71 |