Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
656 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 656 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 |
|---|---|---|
| 9. #564×C71 | C4 | semidirect |
| 64. C71 | #8509 | semidirect |
| 66. #564 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589310 | 2 |
| C2×#17985741 | 2 |
| C2×#564×C71 | 2 |
| #8509 | 71 |