Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
484 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 484 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. #22589314 | C2 | semidirect |
| 4. #22586904 | C2 | semidirect |
| 6. #22586184 | C2 | semidirect |
| 7. C71×#3209 | C2 | semidirect |
| 181. #3209 | D71 | semidirect |
| 187. C71 | #10223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599468 | 2 |
| #22598688 | 2 |
| #22589314 | 2 |
| #22586904 | 2 |
| #22586901 | 2 |
| #22586184 | 2 |
| C71×#3209 | 2 |
| #10223 | 71 |