Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
420 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 110 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. #22625137 | C2 | semidirect |
| 4. #22625127 | C2 | semidirect |
| 5. #22624763 | C2 | semidirect |
| 6. #22624762 | C2 | semidirect |
| 171. C73 | #8189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626616 | 2 |
| #22625225 | 2 |
| #22625137 | 2 |
| #22625127 | 2 |
| #22624763 | 2 |
| #22624762 | 2 |
| #22608312 | 2 |
| #8189 | 73 |