Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
2878 conjugacy classes of subgroups; only the 491 normal subgroups are shown.
This group has 2878 conjugacy classes of subgroups — too many to draw. Only its 491 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. #22586577 | C2 | semidirect |
| 5. C22×C4×Dic71 | C22 | semidirect |
| 6. #17985855 | C4 | semidirect |
| 7. C2×C71⋊#95 | C22 | semidirect |
| 10. #379×C71 | C4 | semidirect |
| 34. C24×C71 | C42 | semidirect |
| 82. C71 | #13827 | semidirect |
| 88. #379 | Dic71 | semidirect |
| 108. 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 |
| #22586577 | 2 |
| C2×#379×C71 | 2 |
| #13827 | 71 |