Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
428 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 428 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 |
|---|---|---|
| 3. #22626148 | C2 | semidirect |
| 4. #22625737 | C2 | semidirect |
| 5. #22625013 | C2 | semidirect |
| 6. #22624998 | C2 | semidirect |
| 13. #17989504 | C4 | semidirect |
| 14. #17989502 | C4 | semidirect |
| 20. #17988700 | C4 | semidirect |
| 21. #17988698 | C4 | semidirect |
| 22. #17988694 | C4 | semidirect |
| 28. #441×C73 | C4 | semidirect |
| 32. #14556666 | C2×C4 | semidirect |
| 36. #14556664 | C2×C4 | semidirect |
| 37. #14556662 | C2×C4 | semidirect |
| 40. #14556659 | C2×C4 | semidirect |
| 185. C73 | #12649 | semidirect |
| 193. #441 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626253 | 2 |
| #22626247 | 2 |
| #22626148 | 2 |
| #22625737 | 2 |
| #22625013 | 2 |
| #22624998 | 2 |
| #22618730 | 2 |
| #12649 | 73 |