Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
706 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22607860 | C2 | semidirect |
| 67. C22×Dic73 | M16 | semidirect |
| 193. C73 | #11500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988448 | 2 |
| #22608258 | 2 |
| #22607860 | 2 |
| C73×#1462 | 2 |
| #11500 | 73 |