Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
786 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 171 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. #22587668 | C2 | semidirect |
| 140. C71 | #19008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599546 | 2 |
| #22598889 | 2 |
| #22587668 | 2 |
| #22586967 | 2 |
| #22586942 | 2 |
| C2×#564×C71 | 2 |
| #19008 | 71 |