Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
444 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 2. #22625588 | C2 | semidirect |
| 4. #22625132 | C2 | semidirect |
| 5. #22624826 | C2 | semidirect |
| 6. #22624819 | C2 | semidirect |
| 8. #17989638 | C4 | semidirect |
| 9. Q8×#10596833 | C4 | semidirect |
| 10. #17989621 | C4 | semidirect |
| 12. #17989615 | C4 | semidirect |
| 22. #17989444 | C4 | semidirect |
| 23. #17989443 | C4 | semidirect |
| 195. C73 | #8247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626747 | 2 |
| #22625588 | 2 |
| #22625384 | 2 |
| #22625132 | 2 |
| #22624826 | 2 |
| #22624819 | 2 |
| #22608416 | 2 |
| #8247 | 73 |