Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
422 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22589749 | C2 | semidirect |
| 4. #22586166 | C2 | semidirect |
| 5. #22586165 | C2 | semidirect |
| 7. C71×#2072 | C2 | semidirect |
| 196. #2072 | D71 | semidirect |
| 200. C71 | #7821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596284 | 2 |
| #22589869 | 2 |
| #22589749 | 2 |
| #22586166 | 2 |
| #22586165 | 2 |
| #22586160 | 2 |
| C71×#2072 | 2 |
| #7821 | 71 |