Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #22610908 | C2 | semidirect |
| 5. #22608351 | C2 | semidirect |
| 6. #22607822 | C2 | semidirect |
| 7. C73×#1276 | C2 | semidirect |
| 11. #17988873 | C4 | semidirect |
| 12. #17988868 | C4 | semidirect |
| 13. #17988798 | C4 | semidirect |
| 14. #17988793 | C4 | semidirect |
| 212. #1276 | D73 | semidirect |
| 213. C73 | #8971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620003 | 2 |
| #22619052 | 2 |
| #22610908 | 2 |
| C4×#14556519 | 2 |
| #22608351 | 2 |
| #22607822 | 2 |
| C73×#1276 | 2 |
| #8971 | 73 |