Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
174 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 174 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 |
|---|---|---|
| 7. #17985829 | C4 | semidirect |
| 12. M64×C71 | C4 | semidirect |
| 78. C71 | #7478 | semidirect |
| 83. M64 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985829 | 2 |
| C2×#17985825 | 2 |
| C2×M64×C71 | 2 |
| #7478 | 71 |