Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
350 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. #22589093 | C2 | semidirect |
| 5. #22586446 | C2 | semidirect |
| 6. #22586439 | C2 | semidirect |
| 7. C2×#347×C71 | C2 | semidirect |
| 16. #17985801 | C4 | semidirect |
| 139. C2×#347 | D71 | semidirect |
| 144. C71 | #13155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985813 | 2 |
| #22590057 | 2 |
| #22589216 | 2 |
| #22589093 | 2 |
| #22586446 | 2 |
| #22586439 | 2 |
| C2×#347×C71 | 2 |
| #13155 | 71 |