Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
290 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 50 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. #17989496 | C4 | semidirect |
| 9. #17989494 | C4 | semidirect |
| 13. C2×#14556502 | C4 | semidirect |
| 14. #384×C73 | C4 | semidirect |
| 133. C73 | #7508 | semidirect |
| 140. #384 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989496 | 2 |
| C2×#17989494 | 2 |
| #22610745 | 2 |
| #7508 | 73 |