Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1938 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1938 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
|---|---|---|
| 1. C2×#17986799 | C2 | semidirect |
| 2. C2×#17985967 | C2 | semidirect |
| 3. #22589445 | C2 | direct (N × H) |
| 4. C2×#338×C71 | C2 | semidirect |
| 8. #17986799 | C22 | semidirect |
| 14. #17985967 | C22 | semidirect |
| 17. #338×C71 | C22 | semidirect |
| 145. C2×C71 | #2017 | semidirect |
| 151. C2×#338 | D71 | semidirect |
| 152. C71 | C2×#2017 | semidirect |
| 165. #338 | C2×D71 | semidirect |
| 293. C2 | #22589445 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986799 | 2 |
| C2×#17985967 | 2 |
| #22589445 | 2 |
| C2×#338×C71 | 2 |
| C2×#2017 | 71 |