Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
336 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22623021 | C2 | semidirect |
| 2. #22612197 | C2 | semidirect |
| 3. #22611967 | C2 | semidirect |
| 4. #22609415 | C2 | semidirect |
| 5. #22607975 | C2 | semidirect |
| 6. #22607899 | C2 | semidirect |
| 7. C73×#1338 | C2 | semidirect |
| 167. #1338 | D73 | semidirect |
| 169. C73 | #12336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623021 | 2 |
| #22612197 | 2 |
| #22611967 | 2 |
| #22609415 | 2 |
| #22607975 | 2 |
| #22607899 | 2 |
| C73×#1338 | 2 |
| #12336 | 73 |