Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
422 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 113 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×#17985828 | C2 | semidirect |
| 3. C2×#17985815 | C2 | semidirect |
| 5. #22589937 | C2 | semidirect |
| 7. C71×#1979 | C2 | semidirect |
| 12. C2×#14556071 | C4 | semidirect |
| 165. #1979 | D71 | semidirect |
| 167. C71 | #13246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556071 | 2 |
| C2×#17985828 | 2 |
| C2×#17985815 | 2 |
| C2×#17985811 | 2 |
| #22589937 | 2 |
| #22589250 | 2 |
| C71×#1979 | 2 |
| #13246 | 71 |