Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 462 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 |
|---|---|---|
| 2. #22591146 | C2 | semidirect |
| 5. #22586205 | C2 | semidirect |
| 6. #22586197 | C2 | semidirect |
| 7. C71×#1528 | C2 | semidirect |
| 9. #17986409 | C4 | semidirect |
| 10. #17986365 | C4 | semidirect |
| 201. #1528 | D71 | semidirect |
| 205. C71 | #9382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599530 | 2 |
| #22591146 | 2 |
| #22589259 | 2 |
| #22586888 | 2 |
| #22586205 | 2 |
| #22586197 | 2 |
| C71×#1528 | 2 |
| #9382 | 71 |