Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
474 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 20. C22×#10596842 | C8 | semidirect |
| 22. C22⋊#10596842 | C8 | semidirect |
| 33. C22⋊#10596833 | C8 | semidirect |
| 37. C22⋊#10596831 | C8 | semidirect |
| 39. C22⋊C8×C73 | C8 | semidirect |
| 175. C73 | #7016 | semidirect |
| 209. C22⋊C8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C22⋊#10596842 | 2 |
| C2×(C2×#10596842)⋊C4 | 2 |
| C22⋊C8×#64408 | 2 |
| #7016 | 73 |