Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
478 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22586975 | C2 | semidirect |
| 3. #22586487 | C2 | semidirect |
| 4. C71×#2132 | C2 | semidirect |
| 15. #17985739 | C22 | semidirect |
| 19. #355×C71 | C22 | semidirect |
| 174. #2132 | D71 | semidirect |
| 177. C71 | #13566 | semidirect |
| 190. #355 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597688 | 2 |
| #22586975 | 2 |
| #22586487 | 2 |
| C71×#2132 | 2 |
| #13566 | 71 |