Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
684 conjugacy classes of subgroups; only the 340 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 340 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. #22626274 | C2 | semidirect |
| 3. C2×#17989510 | C2 | semidirect |
| 88. C73 | #33401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626898 | 2 |
| #22626274 | 2 |
| C2×#17989510 | 2 |
| C4×#14556598 | 2 |
| #33401 | 73 |