Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
706 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 96 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. #22626107 | C2 | semidirect |
| 2. #22625703 | C2 | semidirect |
| 3. #22625404 | C2 | semidirect |
| 6. #22625274 | C2 | semidirect |
| 22. #17989315 | C4 | semidirect |
| 24. #17989310 | C4 | semidirect |
| 29. #17989252 | C4 | semidirect |
| 38. #557×C73 | C4 | semidirect |
| 283. C73 | #8417 | semidirect |
| 286. #557 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626107 | 2 |
| #22625703 | 2 |
| #22625404 | 2 |
| #22625383 | 2 |
| #22625335 | 2 |
| #22625274 | 2 |
| #22624024 | 2 |
| #8417 | 73 |