Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
420 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. #22586977 | C2 | semidirect |
| 4. #22586890 | C2 | semidirect |
| 6. #22586212 | C2 | semidirect |
| 7. C71×#1288 | C2 | semidirect |
| 10. #17986404 | C4 | semidirect |
| 11. #17986372 | C4 | semidirect |
| 12. #17986350 | C4 | semidirect |
| 13. #17986346 | C4 | semidirect |
| 166. #1288 | D71 | semidirect |
| 167. C71 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599058 | 2 |
| #22597410 | 2 |
| #22586977 | 2 |
| #22586890 | 2 |
| #22586886 | 2 |
| #22586212 | 2 |
| C71×#1288 | 2 |
| #9415 | 71 |