Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
872 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 224 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. #22625422 | C2 | semidirect |
| 4. #22625395 | C2 | semidirect |
| 5. #22625393 | C2 | semidirect |
| 6. #22625388 | C2 | semidirect |
| 169. C73 | #17692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626777 | 2 |
| #22625422 | 2 |
| #22625395 | 2 |
| #22625393 | 2 |
| #22625388 | 2 |
| #22623753 | 2 |
| #17692 | 73 |