Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
298 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 1. C2×#17989518 | C2 | semidirect |
| 2. #22626282 | C2 | semidirect |
| 3. #22625081 | C2 | semidirect |
| 4. #22625080 | C2 | semidirect |
| 13. #17989020 | C4 | semidirect |
| 14. #17989019 | C4 | semidirect |
| 17. #17989016 | C4 | semidirect |
| 22. #508×C73 | C4 | semidirect |
| 142. C73 | #13615 | semidirect |
| 149. #508 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989518 | 2 |
| #22626282 | 2 |
| #22625081 | 2 |
| #22625080 | 2 |
| #508×D73 | 2 |
| #13615 | 73 |