Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
406 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22586956 | C2 | semidirect |
| 5. #22586762 | C2 | semidirect |
| 6. #22586238 | C2 | semidirect |
| 7. C71×#1291 | C2 | semidirect |
| 188. #1291 | D71 | semidirect |
| 189. C71 | #9314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598503 | 2 |
| #22596992 | 2 |
| #22586956 | 2 |
| #22586772 | 2 |
| #22586762 | 2 |
| #22586238 | 2 |
| C71×#1291 | 2 |
| #9314 | 71 |