Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
420 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 72 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. #22625423 | C2 | semidirect |
| 3. #22625355 | C2 | semidirect |
| 5. #22624798 | C2 | semidirect |
| 6. #22624791 | C2 | semidirect |
| 20. #17988960 | C4 | semidirect |
| 21. #17988939 | C4 | semidirect |
| 22. #17988935 | C4 | semidirect |
| 26. #500×C73 | C4 | semidirect |
| 167. C73 | #9415 | semidirect |
| 170. #500 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626818 | 2 |
| #22625423 | 2 |
| #22625355 | 2 |
| #22625352 | 2 |
| #22624798 | 2 |
| #22624791 | 2 |
| #22620651 | 2 |
| #9415 | 73 |