Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
490 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22590005 | C2 | semidirect |
| 3. #22586486 | C2 | semidirect |
| 4. C71×#1560 | C2 | semidirect |
| 5. #17986835 | C4 | semidirect |
| 8. #17986176 | C4 | semidirect |
| 12. #17985983 | C4 | semidirect |
| 15. #17985792 | C22 | semidirect |
| 19. #331×C71 | C22 | semidirect |
| 180. #1560 | D71 | semidirect |
| 182. C71 | #13562 | semidirect |
| 197. #331 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597688 | 2 |
| #22590005 | 2 |
| #22586486 | 2 |
| C71×#1560 | 2 |
| #13562 | 71 |