Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
558 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 147 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×#17985801 | C2 | semidirect |
| 3. #22588369 | C2 | semidirect |
| 4. #22586432 | C2 | semidirect |
| 5. C22×M32×C71 | C2 | semidirect |
| 9. #17986235 | C4 | semidirect |
| 48. C2×C16×C71 | D4 | semidirect |
| 146. C22×M32 | D71 | semidirect |
| 151. C71 | #13061 | semidirect |
| 188. C2×C16 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986235 | 2 |
| C2×#17985801 | 2 |
| #22588369 | 2 |
| #22586432 | 2 |
| C22×M32×C71 | 2 |
| #13061 | 71 |