Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
374 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22612183 | C2 | semidirect |
| 3. #22611973 | C2 | semidirect |
| 4. #22607979 | C2 | semidirect |
| 5. #22607891 | C2 | semidirect |
| 6. D4⋊#11924003 | C2 | semidirect |
| 7. C73×#1669 | C2 | semidirect |
| 147. #1669 | D73 | semidirect |
| 151. C73 | #12323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621653 | 2 |
| #22612183 | 2 |
| #22611973 | 2 |
| #22607979 | 2 |
| #22607891 | 2 |
| D4⋊#11924003 | 2 |
| C73×#1669 | 2 |
| #12323 | 73 |