Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
412 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22587131 | C2 | semidirect |
| 5. #22586172 | C2 | semidirect |
| 6. #22586172 | C2 | semidirect |
| 7. C71×#1574 | C2 | semidirect |
| 20. #17985747 | C4 | semidirect |
| 21. #17985747 | C4 | semidirect |
| 22. #17985742 | C4 | semidirect |
| 23. #17985742 | C4 | semidirect |
| 166. #1574 | D71 | semidirect |
| 170. C71 | #8934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597406 | 2 |
| #22589167 | 2 |
| #22587131 | 2 |
| #22587000 | 2 |
| #22586172 | 2 |
| C71×#1574 | 2 |
| #8934 | 71 |