Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
458 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 458 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. #22619021 | C2 | semidirect |
| 3. #22609764 | C2 | semidirect |
| 6. #22607829 | C2 | semidirect |
| 7. C73×#1285 | C2 | semidirect |
| 11. #17988883 | C4 | semidirect |
| 12. #17988883 | C4 | semidirect |
| 13. #17988788 | C4 | semidirect |
| 14. #17988788 | C4 | semidirect |
| 210. #1285 | D73 | semidirect |
| 211. C73 | #9164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620054 | 2 |
| #22619021 | 2 |
| #22609764 | 2 |
| #22608543 | 2 |
| #22608425 | 2 |
| #22607829 | 2 |
| C73×#1285 | 2 |
| #9164 | 73 |