Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
900 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 900 conjugacy classes of subgroups — too many to draw. Only its 228 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. #22625470 | C2 | semidirect |
| 4. #22625446 | C2 | semidirect |
| 5. #22625440 | C2 | semidirect |
| 6. #22625436 | C2 | semidirect |
| 178. C73 | #17777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626863 | 2 |
| #22625470 | 2 |
| #22625446 | 2 |
| #22625440 | 2 |
| #22625436 | 2 |
| #22623744 | 2 |
| #17777 | 73 |