Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22586904 | C2 | semidirect |
| 5. #22586238 | C2 | semidirect |
| 6. #22586222 | C2 | semidirect |
| 7. C71×#1531 | C2 | semidirect |
| 9. #17986405 | C4 | semidirect |
| 10. #17986391 | C4 | semidirect |
| 11. #17986367 | C4 | semidirect |
| 12. #17986361 | C4 | semidirect |
| 201. #1531 | D71 | semidirect |
| 206. C71 | #9431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599043 | 2 |
| #22597334 | 2 |
| #22586904 | 2 |
| #22586879 | 2 |
| #22586238 | 2 |
| #22586222 | 2 |
| C71×#1531 | 2 |
| #9431 | 71 |