Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
726 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 176 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 |
|---|---|---|
| 2. #22624809 | C2 | semidirect |
| 5. #17989610 | C4 | semidirect |
| 18. #14556658 | C2×C4 | semidirect |
| 129. C73 | #8040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989610 | 2 |
| #22624809 | 2 |
| #384×D73 | 2 |
| #8040 | 73 |