Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
702 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 86 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. C22×#14556652 | C2 | semidirect |
| 2. C2×#17989495 | C2 | semidirect |
| 3. #22625765 | C2 | semidirect |
| 4. #22625029 | C2 | semidirect |
| 36. #14556652 | D4 | semidirect |
| 210. C22×C73 | #355 | semidirect |
| 238. C73 | #13092 | semidirect |
| 443. C22 | #17989495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556652 | 2 |
| C2×#17989495 | 2 |
| #22625765 | 2 |
| #22625029 | 2 |
| #22613590 | 2 |
| #13092 | 73 |