Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1312 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1312 conjugacy classes of subgroups — too many to draw. Only its 271 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. #22596819 | C2 | semidirect |
| 3. #22590031 | C2 | semidirect |
| 4. #22590023 | C2 | semidirect |
| 5. C71×#2888 | C2 | semidirect |
| 17. #17985983 | C22 | semidirect |
| 19. #17985797 | C22 | semidirect |
| 20. #17985795 | C22 | semidirect |
| 23. #413×C71 | C22 | semidirect |
| 187. #2888 | D71 | semidirect |
| 190. C71 | #33373 | semidirect |
| 205. #413 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602114 | 2 |
| #22596819 | 2 |
| #22590031 | 2 |
| #22590023 | 2 |
| C71×#2888 | 2 |
| #33373 | 71 |