Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
456 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#17985814 | C2 | semidirect |
| 4. #22589255 | C2 | semidirect |
| 5. #22586453 | C2 | semidirect |
| 6. #22586426 | C2 | semidirect |
| 10. #17986439 | C4 | semidirect |
| 174. C71 | #13031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986439 | 2 |
| #22590089 | 2 |
| C2×#17985814 | 2 |
| #22589255 | 2 |
| #22586453 | 2 |
| #22586426 | 2 |
| C71×#2957 | 2 |
| #13031 | 71 |