Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1198 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 224 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. #22626233 | C2 | direct (N × H) |
| 3. C2×#17989497 | C2 | semidirect |
| 10. #17989497 | C22 | semidirect |
| 185. C2×C73 | #2135 | semidirect |
| 192. C73 | C2×#2135 | semidirect |
| 373. C2 | #22626233 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989573 | 2 |
| #22626233 | 2 |
| C2×#17989497 | 2 |
| C2×#17989161 | 2 |
| C2×#2135 | 73 |