Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
926 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 110 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×#17989506 | C2 | semidirect |
| 2. C2×#17989505 | C2 | semidirect |
| 3. #22626159 | C2 | semidirect |
| 4. #22625810 | C2 | semidirect |
| 243. C73 | #12738 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989506 | 2 |
| C2×#17989505 | 2 |
| #22626159 | 2 |
| #22625810 | 2 |
| C2×#135×D73 | 2 |
| #12738 | 73 |