Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22619101 | C2 | semidirect |
| 3. #22610763 | C2 | semidirect |
| 4. #22608401 | C2 | semidirect |
| 5. #22607824 | C2 | semidirect |
| 6. #22607822 | C2 | semidirect |
| 7. C73×#1500 | C2 | semidirect |
| 9. #17988997 | C4 | semidirect |
| 10. #17988977 | C4 | semidirect |
| 11. #17988953 | C4 | semidirect |
| 12. #17988946 | C4 | semidirect |
| 219. #1500 | D73 | semidirect |
| 223. C73 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620527 | 2 |
| #22619101 | 2 |
| #22610763 | 2 |
| #22608401 | 2 |
| #22607824 | 2 |
| #22607822 | 2 |
| C73×#1500 | 2 |
| #8997 | 73 |