Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
356 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22611727 | C2 | semidirect |
| 3. #22609819 | C2 | semidirect |
| 4. #22607943 | C2 | semidirect |
| 7. C73×#1348 | C2 | semidirect |
| 9. #17988988 | C4 | semidirect |
| 10. #17988972 | C4 | semidirect |
| 14. Q16×Dic73 | C4 | semidirect |
| 16. #17988669 | C4 | semidirect |
| 166. #1348 | D73 | semidirect |
| 169. C73 | #11741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620502 | 2 |
| #22611727 | 2 |
| #22609819 | 2 |
| #22607943 | 2 |
| #22607941 | 2 |
| #22607939 | 2 |
| C73×#1348 | 2 |
| #11741 | 73 |