Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1092 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×#17989337 | C2 | semidirect |
| 2. C2×#17988770 | C2 | semidirect |
| 3. #22611951 | C2 | direct (N × H) |
| 4. C2×#17988385 | C2 | semidirect |
| 5. C2×#17988384 | C2 | semidirect |
| 10. #17989337 | C22 | semidirect |
| 17. #17988770 | C22 | semidirect |
| 20. #17988385 | C22 | semidirect |
| 21. #17988384 | C22 | semidirect |
| 219. C2×C73 | #2203 | semidirect |
| 227. C73 | C2×#2203 | semidirect |
| 439. C2 | #22611951 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989337 | 2 |
| C2×#17988770 | 2 |
| #22611951 | 2 |
| C2×#17988385 | 2 |
| C2×#17988384 | 2 |
| C2×#454×C73 | 2 |
| C2×#2203 | 73 |