Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
466 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 98 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. #22626042 | C2 | semidirect |
| 4. #22625724 | C2 | semidirect |
| 5. #22624810 | C2 | semidirect |
| 6. #22624760 | C2 | semidirect |
| 23. #17988331 | C4 | semidirect |
| 24. #17988330 | C4 | semidirect |
| 25. #17988330 | C4 | semidirect |
| 26. #331×C73 | C4 | semidirect |
| 225. C73 | #9563 | semidirect |
| 244. #331 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626098 | 2 |
| #22626059 | 2 |
| #22626042 | 2 |
| #22625724 | 2 |
| #22624810 | 2 |
| #22624760 | 2 |
| #331×D73 | 2 |
| #9563 | 73 |