Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1066 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 170 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. #22626495 | C2 | semidirect |
| 3. C2×#17989468 | C2 | semidirect |
| 4. #22625637 | C2 | semidirect |
| 9. #17989557 | C4 | semidirect |
| 81. C2×#10596833 | C22⋊C4 | semidirect |
| 227. C73 | #10937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989557 | 2 |
| #22626495 | 2 |
| C2×#17989468 | 2 |
| #22625637 | 2 |
| #22612309 | 2 |
| #10937 | 73 |