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. #22610851 | C2 | semidirect |
| 3. #22610849 | C2 | semidirect |
| 4. C4×#14556522 | C2 | semidirect |
| 5. #22608427 | C2 | semidirect |
| 6. #22608221 | C2 | semidirect |
| 7. C73×#1502 | C2 | semidirect |
| 9. #17988990 | C4 | semidirect |
| 10. #17988963 | C4 | semidirect |
| 11. #17988935 | C4 | semidirect |
| 12. #17988933 | C4 | semidirect |
| 171. #10596831 | #104 | semidirect |
| 207. #1502 | 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 |
| #22610851 | 2 |
| #22610849 | 2 |
| C4×#14556522 | 2 |
| #22608427 | 2 |
| #22608221 | 2 |
| C73×#1502 | 2 |
| #9721 | 73 |