Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
272 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 19. #367×C71 | C4 | semidirect |
| 20. #366×C71 | C4 | semidirect |
| 129. C71 | #13118 | semidirect |
| 139. #367 | Dic71 | semidirect |
| 140. #366 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589079 | 2 |
| #22588226 | 2 |
| #22586448 | 2 |
| #22586445 | 2 |
| #22586439 | 2 |
| #22586419 | 2 |
| C71×#2159 | 2 |
| #13118 | 71 |