Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
432 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 95 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×#17985820 | C2 | semidirect |
| 3. C2×#17985812 | C2 | semidirect |
| 4. #22590050 | C2 | semidirect |
| 5. #22589228 | C2 | semidirect |
| 6. #22586448 | C2 | semidirect |
| 7. C71×#1970 | C2 | semidirect |
| 182. #1970 | 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×#17986435 | 2 |
| C2×#17985820 | 2 |
| C2×#17985812 | 2 |
| #22590050 | 2 |
| #22589228 | 2 |
| #22586448 | 2 |
| C71×#1970 | 2 |
| #13445 | 71 |