Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
2286 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 2286 conjugacy classes of subgroups — too many to draw. Only its 555 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. #22586567 | C2 | semidirect |
| 12. C22×C42×C71 | C4 | semidirect |
| 99. C71 | #14684 | semidirect |
| 104. C22×C42 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985862 | 2 |
| #22586567 | 2 |
| #22586563 | 2 |
| C23×C42×C71 | 2 |
| #14684 | 71 |