Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
510 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22609710 | C2 | semidirect |
| 4. #22607816 | C2 | semidirect |
| 5. C73×#1298 | C2 | semidirect |
| 6. C2×#14556599 | C4 | semidirect |
| 11. #17988615 | C4 | semidirect |
| 12. #17988555 | C4 | semidirect |
| 13. #17988545 | C4 | semidirect |
| 17. #17988325 | C4 | semidirect |
| 18. #17988322 | C4 | semidirect |
| 147. #1298 | D73 | semidirect |
| 149. C73 | #8239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618621 | 2 |
| #22609710 | 2 |
| #22608423 | 2 |
| #22607816 | 2 |
| C73×#1298 | 2 |
| #8239 | 73 |