Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1082 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 1. #22625787 | C2 | semidirect |
| 2. C2×#17989447 | C2 | semidirect |
| 3. C2×#17989445 | C2 | semidirect |
| 222. C73 | #8344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625787 | 2 |
| C2×#17989447 | 2 |
| C2×#17989445 | 2 |
| C2×#17989133 | 2 |
| #8344 | 73 |