Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
312 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 74 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. #22626143 | C2 | semidirect |
| 4. #22626051 | C2 | semidirect |
| 5. #22625012 | C2 | semidirect |
| 6. #22624994 | C2 | semidirect |
| 23. #17988404 | C4 | semidirect |
| 24. #17988402 | C4 | semidirect |
| 25. #17988400 | C4 | semidirect |
| 26. #361×C73 | C4 | semidirect |
| 159. C73 | #13146 | semidirect |
| 173. #361 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989501 | 2 |
| #22626143 | 2 |
| #22626088 | 2 |
| #22626051 | 2 |
| #22625012 | 2 |
| #22624994 | 2 |
| #22611677 | 2 |
| #13146 | 73 |