Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
422 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 113 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. #17986378 | C4 | semidirect |
| 10. #17986351 | C4 | semidirect |
| 78. C2×C71⋊C8 | Q16 | semidirect |
| 163. C71 | #9290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599285 | 2 |
| #22597281 | 2 |
| #22589312 | 2 |
| #22587024 | 2 |
| #22586198 | 2 |
| #22586170 | 2 |
| C71×#1518 | 2 |
| #9290 | 71 |