Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
320 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22611606 | C2 | semidirect |
| 3. #22608107 | C2 | semidirect |
| 4. #22608089 | C2 | semidirect |
| 5. C73×#2133 | C2 | semidirect |
| 6. #17989192 | C4 | semidirect |
| 8. #17988961 | C4 | semidirect |
| 9. #17988955 | C4 | semidirect |
| 15. #17988648 | C4 | semidirect |
| 150. #2133 | D73 | semidirect |
| 154. C73 | #13606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620992 | 2 |
| #22611606 | 2 |
| #22608107 | 2 |
| #22608089 | 2 |
| C73×#2133 | 2 |
| #13606 | 73 |