Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22610019 | C2 | semidirect |
| 4. #22610009 | C2 | semidirect |
| 5. #22607837 | C2 | semidirect |
| 6. #22607807 | C2 | semidirect |
| 10. #17988915 | C4 | semidirect |
| 12. #17988898 | C4 | semidirect |
| 222. C73 | #9521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619851 | 2 |
| #22618979 | 2 |
| #22610019 | 2 |
| #22610009 | 2 |
| #22607837 | 2 |
| #22607807 | 2 |
| C73×#1513 | 2 |
| #9521 | 73 |