Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
498 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22610850 | C2 | semidirect |
| 3. C4×#14556522 | C2 | semidirect |
| 4. #22608426 | C2 | semidirect |
| 5. #22608425 | C2 | semidirect |
| 6. #22608218 | C2 | semidirect |
| 7. C73×#1980 | C2 | semidirect |
| 9. #17988990 | C4 | semidirect |
| 10. #17988963 | C4 | semidirect |
| 11. #17988935 | C4 | semidirect |
| 12. #17988933 | C4 | semidirect |
| 171. #10596831 | #104 | semidirect |
| 204. #1980 | D73 | semidirect |
| 209. C73 | #9721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620506 | 2 |
| #22610850 | 2 |
| C4×#14556522 | 2 |
| #22608426 | 2 |
| #22608425 | 2 |
| #22608218 | 2 |
| C73×#1980 | 2 |
| #9721 | 73 |