Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22610652 | C2 | semidirect |
| 5. #22607832 | C2 | semidirect |
| 6. #22607775 | C2 | semidirect |
| 7. C73×#1570 | C2 | semidirect |
| 167. #1570 | D73 | semidirect |
| 172. C73 | #8880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618648 | 2 |
| #22610652 | 2 |
| #22608427 | 2 |
| #22608329 | 2 |
| #22607832 | 2 |
| #22607775 | 2 |
| C73×#1570 | 2 |
| #8880 | 73 |