Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
412 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 93 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×#17985811 | C2 | semidirect |
| 3. C2×#17985801 | C2 | semidirect |
| 4. #22589953 | C2 | semidirect |
| 5. #22588401 | C2 | semidirect |
| 6. #22586450 | C2 | semidirect |
| 7. C2×#368×C71 | C2 | semidirect |
| 172. C2×#368 | D71 | semidirect |
| 178. C71 | #13393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986270 | 2 |
| C2×#17985811 | 2 |
| C2×#17985801 | 2 |
| #22589953 | 2 |
| #22588401 | 2 |
| #22586450 | 2 |
| C2×#368×C71 | 2 |
| #13393 | 71 |