Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
456 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 106 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. #22626900 | C2 | semidirect |
| 2. #22626173 | C2 | semidirect |
| 3. C2×#17989486 | C2 | semidirect |
| 4. #22626161 | C2 | semidirect |
| 5. #22624985 | C2 | semidirect |
| 6. #22624981 | C2 | semidirect |
| 185. C73 | #12979 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626900 | 2 |
| #22626173 | 2 |
| C2×#17989486 | 2 |
| #22626161 | 2 |
| #22624985 | 2 |
| #22624981 | 2 |
| #22618830 | 2 |
| #12979 | 73 |