Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
314 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 4. #22588226 | C2 | semidirect |
| 5. #22586443 | C2 | semidirect |
| 6. #22586423 | C2 | semidirect |
| 7. C71×#2155 | C2 | semidirect |
| 15. #17985816 | C4 | semidirect |
| 16. #17985813 | C4 | semidirect |
| 139. #2155 | D71 | semidirect |
| 146. C71 | #13140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590090 | 2 |
| #22590075 | 2 |
| #22589231 | 2 |
| #22588226 | 2 |
| #22586443 | 2 |
| #22586423 | 2 |
| C71×#2155 | 2 |
| #13140 | 71 |