Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
2286 conjugacy classes of subgroups; only the 947 normal subgroups are shown.
This group has 2286 conjugacy classes of subgroups — too many to draw. Only its 947 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 |
|---|---|---|
| 10. C42×Dic71 | C4 | semidirect |
| 36. C4×Dic71 | C4⋊C4 | semidirect |
| 46. C42×C71 | C4⋊C4 | semidirect |
| 72. C4×C71 | #384 | semidirect |
| 74. Dic71 | #384 | semidirect |
| 85. C71 | #14692 | semidirect |
| 127. C42 | Dic71⋊C4 | semidirect |
| 155. C4 | #17985868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985869 | 2 |
| C2×#17985868 | 2 |
| C2×C42×Dic71 | 2 |
| C2×#384×C71 | 2 |
| #14692 | 71 |