Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
274 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 7. #17989682 | C4 | semidirect |
| 9. #17989676 | C4 | semidirect |
| 26. #14556660 | C8 | semidirect |
| 34. #14556525 | C8 | semidirect |
| 36. #107×C73 | C8 | semidirect |
| 124. C73 | #7178 | semidirect |
| 150. #107 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989682 | 2 |
| C2×#17989676 | 2 |
| #107×#64408 | 2 |
| #7178 | 73 |