Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
670 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22608056 | C2 | semidirect |
| 8. C2×#117×C73 | C4 | semidirect |
| 9. C22×C42×C73 | C4 | semidirect |
| 10. #391×C73 | C4 | semidirect |
| 129. C73 | #12857 | semidirect |
| 131. C2×#117 | Dic73 | semidirect |
| 132. C22×C42 | Dic73 | semidirect |
| 135. #391 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22609849 | 2 |
| #22608056 | 2 |
| C73×#2297 | 2 |
| #12857 | 73 |