Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
450 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. C2×#17985815 | C2 | semidirect |
| 5. #22586456 | C2 | semidirect |
| 6. #22586444 | C2 | semidirect |
| 7. C71×#2141 | C2 | semidirect |
| 15. #17986271 | C4 | semidirect |
| 165. #2141 | D71 | semidirect |
| 169. C71 | #13069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601442 | 2 |
| C2×#17986271 | 2 |
| C2×#17985815 | 2 |
| #22588391 | 2 |
| #22586456 | 2 |
| #22586444 | 2 |
| C71×#2141 | 2 |
| #13069 | 71 |