Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
694 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 154 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 |
|---|---|---|
| 18. #17988344 | C4 | semidirect |
| 19. #17988343 | C4 | semidirect |
| 20. H(3,ℤ/4)×C73 | C4 | semidirect |
| 166. C73 | #11336 | semidirect |
| 180. H(3,ℤ/4) | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D73⋊#430 | 2 |
| D73⋊#424 | 2 |
| #22625612 | 2 |
| #22625599 | 2 |
| H(3,ℤ/4)×D73 | 2 |
| #11336 | 73 |