Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1114 conjugacy classes of subgroups; only the 380 normal subgroups are shown.
This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 380 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. #22626898 | C2 | semidirect |
| 2. C2×#17989645 | C2 | semidirect |
| 3. #22626173 | C2 | semidirect |
| 4. C2×#17989485 | C2 | semidirect |
| 8. C2×#14556665 | C22 | semidirect |
| 9. C2×#14556665 | C22 | semidirect |
| 10. C22×#11924031 | C22 | semidirect |
| 11. #17989485 | C22 | semidirect |
| 12. #17989485 | C22 | semidirect |
| 120. C73 | #33340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626898 | 2 |
| C2×#17989645 | 2 |
| #22626173 | 2 |
| C2×#17989485 | 2 |
| #22624643 | 2 |
| #33340 | 73 |