Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
570 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22586913 | C2 | semidirect |
| 4. #22586220 | C2 | semidirect |
| 8. #17985938 | C4 | semidirect |
| 9. #17985935 | C4 | semidirect |
| 10. #17985919 | C4 | semidirect |
| 11. #17985911 | C4 | semidirect |
| 199. C71 | #9383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22593516 | 2 |
| #22588328 | 2 |
| #22586913 | 2 |
| #22586220 | 2 |
| C71×#2972 | 2 |
| #9383 | 71 |