Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22588140 | C2 | semidirect |
| 3. #22586463 | C2 | semidirect |
| 4. #22586461 | C2 | semidirect |
| 9. #17985789 | C4 | semidirect |
| 10. #17985786 | C4 | semidirect |
| 13. C23×C8×C71 | C4 | semidirect |
| 17. #424×C71 | C4 | semidirect |
| 19. #407×C71 | C4 | semidirect |
| 20. #405×C71 | C4 | semidirect |
| 154. C71 | #12623 | semidirect |
| 156. C23×C8 | Dic71 | semidirect |
| 160. #424 | Dic71 | semidirect |
| 164. #407 | Dic71 | semidirect |
| 166. #405 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589981 | 2 |
| #22588140 | 2 |
| #22586463 | 2 |
| #22586461 | 2 |
| C71×#2929 | 2 |
| #12623 | 71 |