Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
492 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22589284 | C2 | semidirect |
| 4. #22586851 | C2 | semidirect |
| 6. #22586197 | C2 | semidirect |
| 7. C71×#1300 | C2 | semidirect |
| 11. #17986280 | C4 | semidirect |
| 12. #17986205 | C4 | semidirect |
| 187. #1300 | D71 | semidirect |
| 189. C71 | #9327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598440 | 2 |
| #22590984 | 2 |
| #22589284 | 2 |
| #22586851 | 2 |
| #22586784 | 2 |
| #22586197 | 2 |
| C71×#1300 | 2 |
| #9327 | 71 |