Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
432 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. C2×#17985819 | C2 | semidirect |
| 3. C2×#17985813 | C2 | semidirect |
| 4. #22589229 | C2 | semidirect |
| 5. #22589204 | C2 | semidirect |
| 6. #22586448 | C2 | semidirect |
| 7. C71×#2139 | C2 | semidirect |
| 180. #2139 | D71 | semidirect |
| 184. C71 | #13445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986434 | 2 |
| C2×#17985819 | 2 |
| C2×#17985813 | 2 |
| #22589229 | 2 |
| #22589204 | 2 |
| #22586448 | 2 |
| C71×#2139 | 2 |
| #13445 | 71 |