Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
202 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 5. C2×#14556641 | C4 | semidirect |
| 42. C2×C4×C73 | C32 | semidirect |
| 72. C73 | #7465 | semidirect |
| 112. C2×C4 | #14556641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556641 | 2 |
| C2×C4×#11924003 | 2 |
| #7465 | 73 |