Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
412 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 412 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. #22625751 | C2 | semidirect |
| 5. #22625010 | C2 | semidirect |
| 6. #22625000 | C2 | semidirect |
| 13. #17989506 | C4 | semidirect |
| 14. #17989505 | C4 | semidirect |
| 15. #17989502 | C4 | semidirect |
| 16. #17989501 | C4 | semidirect |
| 198. C73 | #12651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626259 | 2 |
| #22626245 | 2 |
| #22626148 | 2 |
| #22625751 | 2 |
| #22625010 | 2 |
| #22625000 | 2 |
| #444×D73 | 2 |
| #12651 | 73 |