Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
424 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 72 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. #22626755 | C2 | semidirect |
| 2. #22625374 | C2 | semidirect |
| 3. #22625352 | C2 | semidirect |
| 4. #22625252 | C2 | semidirect |
| 5. #22624792 | C2 | semidirect |
| 6. #22624787 | C2 | semidirect |
| 26. #17988979 | C4 | semidirect |
| 27. #17988976 | C4 | semidirect |
| 28. #17988953 | C4 | semidirect |
| 34. #491×C73 | C4 | semidirect |
| 212. C73 | #9370 | semidirect |
| 217. #491 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626755 | 2 |
| #22625374 | 2 |
| #22625352 | 2 |
| #22625252 | 2 |
| #22624792 | 2 |
| #22624787 | 2 |
| #22620971 | 2 |
| #9370 | 73 |