Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
258 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 9. #17985775 | C4 | semidirect |
| 10. C4×C71⋊C16 | C4 | semidirect |
| 16. #347×C71 | C4 | semidirect |
| 83. C71 | #12597 | semidirect |
| 89. #347 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589937 | 2 |
| #22588095 | 2 |
| #22586430 | 2 |
| #22586427 | 2 |
| C71×#2110 | 2 |
| #12597 | 71 |