Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
494 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22586839 | C2 | semidirect |
| 5. #22586242 | C2 | semidirect |
| 6. #22586198 | C2 | semidirect |
| 7. C71×#1518 | C2 | semidirect |
| 10. #17986286 | C4 | semidirect |
| 11. #17986276 | C4 | semidirect |
| 193. #1518 | D71 | semidirect |
| 198. C71 | #9177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598133 | 2 |
| #22591315 | 2 |
| #22586839 | 2 |
| #22586732 | 2 |
| #22586242 | 2 |
| #22586198 | 2 |
| C71×#1518 | 2 |
| #9177 | 71 |