Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1258 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 259 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 |
|---|---|---|
| 3. #22610773 | C2 | semidirect |
| 120. C2×Dic73 | #101 | semidirect |
| 151. C73 | #21799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556589 | 2 |
| #22618560 | 2 |
| #22610773 | 2 |
| #22609855 | 2 |
| #22609854 | 2 |
| C73×#1784 | 2 |
| #21799 | 73 |