Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1114 conjugacy classes of subgroups; only the 391 normal subgroups are shown.
This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 391 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 |
|---|---|---|
| 1. C2×#17986416 | C2 | semidirect |
| 2. #22596951 | C2 | semidirect |
| 3. #22590068 | C2 | semidirect |
| 4. C2×#17985806 | C2 | semidirect |
| 8. C2×#14556068 | C22 | semidirect |
| 9. C22×C71⋊C16 | C22 | semidirect |
| 11. C2×#14556064 | C22 | semidirect |
| 12. #17985806 | C22 | semidirect |
| 13. #17985806 | C22 | semidirect |
| 122. C71 | #33385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986416 | 2 |
| #22596951 | 2 |
| #22590068 | 2 |
| C2×#17985806 | 2 |
| C71×#3584 | 2 |
| #33385 | 71 |