Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
402 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22586891 | C2 | semidirect |
| 5. #22586213 | C2 | semidirect |
| 6. #22586206 | C2 | semidirect |
| 7. C71×#2987 | C2 | semidirect |
| 9. #17986402 | C4 | semidirect |
| 10. #17986373 | C4 | semidirect |
| 11. #17986349 | C4 | semidirect |
| 12. #17986347 | C4 | semidirect |
| 157. #2987 | D71 | semidirect |
| 163. C71 | #9418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599059 | 2 |
| #22586974 | 2 |
| #22586891 | 2 |
| #22586888 | 2 |
| #22586213 | 2 |
| #22586206 | 2 |
| C71×#2987 | 2 |
| #9418 | 71 |