Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
960 conjugacy classes of subgroups; only the 247 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 247 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×#17986047 | C2 | semidirect |
| 3. #22589742 | C2 | semidirect |
| 4. #22589739 | C2 | semidirect |
| 5. C2×#338×C71 | C2 | semidirect |
| 130. C2×#338 | D71 | semidirect |
| 131. C71 | #23622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986047 | 2 |
| C2×#17985981 | 2 |
| #22589742 | 2 |
| #22589739 | 2 |
| C2×#338×C71 | 2 |
| #23622 | 71 |