Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
482 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22590005 | C2 | semidirect |
| 2. #22586975 | C2 | semidirect |
| 3. #22586491 | C2 | semidirect |
| 7. #17985794 | C22 | semidirect |
| 10. #17985739 | C22 | semidirect |
| 11. #585×C71 | C4 | semidirect |
| 14. #456×C71 | C4 | semidirect |
| 19. #413×C71 | C4 | semidirect |
| 178. C71 | #13570 | semidirect |
| 179. #585 | Dic71 | semidirect |
| 182. #456 | Dic71 | semidirect |
| 188. #413 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590005 | 2 |
| #22586975 | 2 |
| #22586491 | 2 |
| C71×#3018 | 2 |
| #13570 | 71 |