Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
334 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 7. #17985792 | C4 | semidirect |
| 9. #17985743 | C4 | semidirect |
| 11. #518×C71 | C4 | semidirect |
| 13. C2×#100×C71 | C4 | semidirect |
| 138. C71 | #7493 | semidirect |
| 140. #518 | Dic71 | semidirect |
| 143. C2×#100 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985792 | 2 |
| #22587054 | 2 |
| C71×#1887 | 2 |
| #7493 | 71 |