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. #22589285 | C2 | semidirect |
| 5. #22586233 | C2 | semidirect |
| 6. #22586195 | C2 | semidirect |
| 7. C71×#1506 | C2 | semidirect |
| 10. #17986276 | C4 | semidirect |
| 11. #17986201 | C4 | semidirect |
| 185. #1506 | 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 |
|---|---|
| #22598435 | 2 |
| #22590984 | 2 |
| #22589285 | 2 |
| #22586782 | 2 |
| #22586233 | 2 |
| #22586195 | 2 |
| C71×#1506 | 2 |
| #9327 | 71 |