Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1166 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 267 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 |
|---|---|---|
| 4. #22588334 | C2 | semidirect |
| 6. #101×Dic71 | C2 | semidirect |
| 135. C71 | #20730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986477 | 2 |
| #22596975 | 2 |
| #22588421 | 2 |
| #22588334 | 2 |
| #22588264 | 2 |
| #101×Dic71 | 2 |
| C71×#1784 | 2 |
| #20730 | 71 |