Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
680 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 171 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. #22618799 | C2 | semidirect |
| 4. #22611995 | C2 | semidirect |
| 5. #22611979 | C2 | semidirect |
| 6. #22611689 | C2 | semidirect |
| 7. #22611651 | C2 | semidirect |
| 9. C22×Q32×C73 | C2 | semidirect |
| 173. C22×Q32 | D73 | semidirect |
| 181. C73 | #33588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989028 | 2 |
| #22620420 | 2 |
| #22618799 | 2 |
| #22611995 | 2 |
| #22611979 | 2 |
| #22611689 | 2 |
| #22611651 | 2 |
| #22611639 | 2 |
| C22×Q32×C73 | 2 |
| #33588 | 73 |