Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22611552 | C2 | semidirect |
| 3. #22607915 | C2 | semidirect |
| 4. C73×#1812 | C2 | semidirect |
| 5. C22×D584 | C4 | semidirect |
| 8. #17988840 | C4 | semidirect |
| 12. #17988625 | C4 | semidirect |
| 15. #17988369 | C22 | semidirect |
| 19. H(3,ℤ/4)×C73 | C22 | semidirect |
| 153. #1812 | D73 | semidirect |
| 155. C73 | #11868 | semidirect |
| 170. H(3,ℤ/4) | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619579 | 2 |
| #22611552 | 2 |
| #22607915 | 2 |
| C73×#1812 | 2 |
| #11868 | 73 |