Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
548 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 84 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. #22626452 | C2 | semidirect |
| 2. #22625362 | C2 | semidirect |
| 3. #22625312 | C2 | semidirect |
| 4. #22625231 | C2 | semidirect |
| 5. #22624827 | C2 | semidirect |
| 6. #22624786 | C2 | semidirect |
| 27. #17988789 | C4 | semidirect |
| 28. #17988783 | C4 | semidirect |
| 29. #17988782 | C4 | semidirect |
| 32. #461×C73 | C4 | semidirect |
| 249. C73 | #9181 | semidirect |
| 256. #461 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626452 | 2 |
| #22625362 | 2 |
| #22625312 | 2 |
| #22625231 | 2 |
| #22624827 | 2 |
| #22624786 | 2 |
| #22619396 | 2 |
| #9181 | 73 |