Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1326 conjugacy classes of subgroups; only the 491 normal subgroups are shown.
This group has 1326 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 |
|---|---|---|
| 7. #17985869 | C4 | semidirect |
| 8. #17985867 | C4 | semidirect |
| 12. #383×C71 | C4 | semidirect |
| 45. C42×C71 | C42 | semidirect |
| 86. C71 | #13830 | semidirect |
| 92. #383 | Dic71 | semidirect |
| 127. C42 | C4×Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985869 | 2 |
| C2×#17985867 | 2 |
| #22586574 | 2 |
| C2×#383×C71 | 2 |
| #13830 | 71 |