Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
642 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 236 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. #22626900 | C2 | semidirect |
| 2. #22626323 | C2 | semidirect |
| 3. #22626320 | C2 | semidirect |
| 4. #22626272 | C2 | semidirect |
| 5. C2×#17989486 | C2 | semidirect |
| 6. #22626142 | C2 | semidirect |
| 9. #17989646 | C22 | semidirect |
| 14. #17989509 | C22 | semidirect |
| 15. #17989486 | C22 | semidirect |
| 16. #17989486 | C22 | semidirect |
| 17. #17989476 | C22 | semidirect |
| 18. #17989473 | C22 | semidirect |
| 129. C73 | #33442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626900 | 2 |
| #22626323 | 2 |
| #22626320 | 2 |
| #22626272 | 2 |
| C2×#17989486 | 2 |
| #22626142 | 2 |
| #22618833 | 2 |
| #33442 | 73 |