Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
242 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 9. #17989450 | C4 | semidirect |
| 11. C4⋊#11924003 | C4 | semidirect |
| 14. C4⋊C16×C73 | C4 | semidirect |
| 103. C73 | #7296 | semidirect |
| 109. C4⋊C16 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556660 | 2 |
| #22625489 | 2 |
| #22611729 | 2 |
| #7296 | 73 |