Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1386 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 235 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. #22618566 | C2 | semidirect |
| 3. #22610777 | C2 | semidirect |
| 4. #22610769 | C2 | semidirect |
| 5. #22609857 | C2 | semidirect |
| 6. #22609852 | C2 | semidirect |
| 7. C73×#1783 | C2 | semidirect |
| 16. #17988610 | C22 | semidirect |
| 17. C2×#14556509 | C22 | semidirect |
| 19. C2×#14556507 | C22 | semidirect |
| 21. M16×Dic73 | C22 | semidirect |
| 165. #1783 | D73 | semidirect |
| 166. C73 | #21801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989154 | 2 |
| #22618566 | 2 |
| #22610777 | 2 |
| #22610769 | 2 |
| #22609857 | 2 |
| #22609852 | 2 |
| C73×#1783 | 2 |
| #21801 | 73 |