Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1614 conjugacy classes of subgroups; only the 296 normal subgroups are shown.
This group has 1614 conjugacy classes of subgroups — too many to draw. Only its 296 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×#17989592 | C2 | semidirect |
| 2. C2×#17989561 | C2 | semidirect |
| 3. C2×#17989546 | C2 | semidirect |
| 4. #22626055 | C2 | semidirect |
| 27. C2×#11924036 | D4 | semidirect |
| 157. C73 | #21188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989592 | 2 |
| C2×#17989561 | 2 |
| C2×#17989546 | 2 |
| #22626055 | 2 |
| C2×#17989135 | 2 |
| #21188 | 73 |