Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
416 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 416 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. #22619026 | C2 | semidirect |
| 5. #22607792 | C2 | semidirect |
| 6. #22607760 | C2 | semidirect |
| 7. C73×#1506 | C2 | semidirect |
| 9. #17988966 | C4 | semidirect |
| 10. #17988961 | C4 | semidirect |
| 11. #17988939 | C4 | semidirect |
| 12. #17988935 | C4 | semidirect |
| 170. #1506 | D73 | semidirect |
| 175. C73 | #9282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620883 | 2 |
| #22619026 | 2 |
| #22608438 | 2 |
| #22608399 | 2 |
| #22607792 | 2 |
| #22607760 | 2 |
| C73×#1506 | 2 |
| #9282 | 73 |