Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1390 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1390 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 |
|---|---|---|
| 1. C2×#17989573 | C2 | semidirect |
| 2. #22626230 | C2 | direct (N × H) |
| 3. C2×#17989495 | C2 | semidirect |
| 7. #17989573 | C22 | semidirect |
| 8. C2×#14556652 | C22 | semidirect |
| 10. #17989495 | C22 | semidirect |
| 27. #14556652 | C23 | semidirect |
| 197. C2×C73 | #2134 | semidirect |
| 204. C73 | C2×#2134 | semidirect |
| 397. C2 | #22626230 | 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 |
| #22626230 | 2 |
| C2×#17989495 | 2 |
| C2×#17989154 | 2 |
| C2×#2134 | 73 |