Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
548 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#17986046 | C2 | semidirect |
| 3. C2×#17985812 | C2 | semidirect |
| 4. C2×#17985780 | C2 | semidirect |
| 5. #22586440 | C2 | semidirect |
| 6. #22586439 | C2 | semidirect |
| 7. C2×#361×C71 | C2 | semidirect |
| 48. #14556064 | D4 | semidirect |
| 66. #108×C71 | D4 | semidirect |
| 182. C2×#361 | D71 | semidirect |
| 186. C71 | #13010 | semidirect |
| 242. #108 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986249 | 2 |
| C2×#17986046 | 2 |
| C2×#17985812 | 2 |
| C2×#17985780 | 2 |
| #22586440 | 2 |
| #22586439 | 2 |
| C2×#361×C71 | 2 |
| #13010 | 71 |