Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
342 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 16. C4⋊#11924003 | C4 | semidirect |
| 17. #17988405 | C4 | semidirect |
| 18. C4⋊C16×C73 | C4 | semidirect |
| 116. C4×C73 | #366 | semidirect |
| 120. Dic73 | #366 | semidirect |
| 136. C73 | #13176 | semidirect |
| 148. C4⋊C16 | #64408 | semidirect |
| 251. C4 | #17989513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989513 | 2 |
| #22625867 | 2 |
| C4×#14556660 | 2 |
| #22624989 | 2 |
| C4⋊C16×D73 | 2 |
| #13176 | 73 |