Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
616 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 1. #22625456 | C2 | semidirect |
| 4. #22625354 | C2 | semidirect |
| 5. #22625353 | C2 | semidirect |
| 6. #22625295 | C2 | semidirect |
| 23. Q8×Dic146 | C4 | semidirect |
| 26. #17989311 | C4 | semidirect |
| 28. #17989297 | C4 | semidirect |
| 38. #557×C73 | C4 | semidirect |
| 258. C73 | #8501 | semidirect |
| 262. #557 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625456 | 2 |
| #22625417 | 2 |
| #22625375 | 2 |
| #22625354 | 2 |
| #22625353 | 2 |
| #22625295 | 2 |
| #22624415 | 2 |
| #8501 | 73 |