Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2038 conjugacy classes of subgroups; only the 1057 normal subgroups are shown.
This group has 2038 conjugacy classes of subgroups — too many to draw. Only its 1057 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. #22627186 | C2 | semidirect |
| 2. #22627185 | C2 | semidirect |
| 3. C2×#17989709 | C2 | semidirect |
| 4. #22627182 | C2 | semidirect |
| 6. #17989709 | C22 | semidirect |
| 7. #17989709 | C22 | semidirect |
| 8. #17989709 | C22 | semidirect |
| 9. #17989708 | C22 | semidirect |
| 10. #17989708 | C22 | semidirect |
| 11. C2×#14556688 | C22 | semidirect |
| 12. #17989706 | C22 | semidirect |
| 13. C2×#14556686 | C22 | semidirect |
| 87. C73 | #62624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627186 | 2 |
| #22627185 | 2 |
| C2×#17989709 | 2 |
| #22627182 | 2 |
| #22626927 | 2 |
| #62624 | 73 |