Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
338 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 30. C4⋊#10596833 | C8 | semidirect |
| 35. C4⋊#10596831 | C8 | semidirect |
| 37. C4⋊C8×C73 | C8 | semidirect |
| 138. C73 | #7027 | semidirect |
| 166. C4⋊C8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊#10596842 | 2 |
| #22627065 | 2 |
| #22625718 | 2 |
| #7027 | 73 |