Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
794 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 2. #22625029 | C2 | semidirect |
| 3. #22625028 | C2 | semidirect |
| 7. #17989574 | C4 | semidirect |
| 25. #14556652 | C2×C4 | semidirect |
| 185. C73 | #12587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989574 | 2 |
| #22625029 | 2 |
| #22625028 | 2 |
| #22612521 | 2 |
| #12587 | 73 |