Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
240 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 36. C22×C4×C73 | C16 | semidirect |
| 95. C73 | #7055 | semidirect |
| 124. C22×C4 | #11924031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22624851 | 2 |
| #22609999 | 2 |
| #7055 | 73 |