Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1422 conjugacy classes of subgroups; only the 443 normal subgroups are shown.
This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 443 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 |
|---|---|---|
| 12. C42×Dic71 | C4 | semidirect |
| 53. C42×C71 | C4⋊C4 | semidirect |
| 87. Dic71 | #383 | semidirect |
| 99. C71 | #14688 | semidirect |
| 147. C42 | Dic71⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985867 | 2 |
| C2×C42×Dic71 | 2 |
| Dic71⋊#95 | 2 |
| #22586566 | 2 |
| C2×#383×C71 | 2 |
| #14688 | 71 |