Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
2734 conjugacy classes of subgroups; only the 411 normal subgroups are shown.
This group has 2734 conjugacy classes of subgroups — too many to draw. Only its 411 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 |
|---|---|---|
| 2. #22586585 | C2 | semidirect |
| 4. C22×C4⋊Dic71 | C22 | semidirect |
| 7. C2×C71⋊#95 | C22 | semidirect |
| 10. #379×C71 | C4 | semidirect |
| 42. C24×C71 | C4⋊C4 | semidirect |
| 106. C71 | #14673 | semidirect |
| 112. #379 | Dic71 | semidirect |
| 140. C24 | C4⋊Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985855 | 2 |
| #22586585 | 2 |
| C2×#379×C71 | 2 |
| #14673 | 71 |