Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1172 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 1172 conjugacy classes of subgroups — too many to draw. Only its 297 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×#17989709 | C2 | semidirect |
| 2. #22627103 | C2 | semidirect |
| 3. #22627099 | C2 | semidirect |
| 4. #22627096 | C2 | semidirect |
| 7. C2×#14556688 | C22 | semidirect |
| 8. C2×#14556686 | C22 | semidirect |
| 9. #17989684 | C22 | semidirect |
| 10. #17989684 | C22 | semidirect |
| 116. C22×C73 | #504 | semidirect |
| 142. C73 | #33334 | semidirect |
| 260. C22 | #17989709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989709 | 2 |
| #22627103 | 2 |
| #22627099 | 2 |
| #22627096 | 2 |
| C22×#14556679 | 2 |
| #33334 | 73 |