Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
544 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 544 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. #22591257 | C2 | semidirect |
| 5. #22586734 | C2 | semidirect |
| 6. #22586241 | C2 | semidirect |
| 7. C71×#1286 | C2 | semidirect |
| 13. #17986210 | C4 | semidirect |
| 14. #17986200 | C4 | semidirect |
| 208. #1286 | D71 | semidirect |
| 209. C71 | #9180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597814 | 2 |
| #22591257 | 2 |
| #22586899 | 2 |
| #22586836 | 2 |
| #22586734 | 2 |
| #22586241 | 2 |
| C71×#1286 | 2 |
| #9180 | 71 |