Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
716 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #22609866 | C2 | semidirect |
| 5. #22607799 | C2 | semidirect |
| 6. #22607798 | C2 | semidirect |
| 7. C73×#1787 | C2 | semidirect |
| 17. #17988506 | C4 | semidirect |
| 18. #17988498 | C4 | semidirect |
| 247. #1787 | D73 | semidirect |
| 250. C73 | #9471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618957 | 2 |
| #22613290 | 2 |
| #22609916 | 2 |
| #22609866 | 2 |
| #22607799 | 2 |
| #22607798 | 2 |
| C73×#1787 | 2 |
| #9471 | 73 |