Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
420 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 3. #22625002 | C2 | semidirect |
| 4. #22625002 | C2 | semidirect |
| 14. #17988625 | C4 | semidirect |
| 19. #107×D73 | C4 | semidirect |
| 20. #107×D73 | C4 | semidirect |
| 22. #427×C73 | C4 | semidirect |
| 162. C73 | #12870 | semidirect |
| 171. #427 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626159 | 2 |
| #22625807 | 2 |
| #22625002 | 2 |
| #427×D73 | 2 |
| #12870 | 73 |