Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
700 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 102 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. #22626110 | C2 | semidirect |
| 3. #22625448 | C2 | semidirect |
| 4. #22625441 | C2 | semidirect |
| 5. #22625313 | C2 | semidirect |
| 22. #17989315 | C4 | semidirect |
| 24. #17989311 | C4 | semidirect |
| 25. #17989310 | C4 | semidirect |
| 38. #557×C73 | C4 | semidirect |
| 295. C73 | #8427 | semidirect |
| 298. #557 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626110 | 2 |
| #22625806 | 2 |
| #22625448 | 2 |
| #22625441 | 2 |
| #22625313 | 2 |
| #22625229 | 2 |
| #22623814 | 2 |
| #8427 | 73 |