Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 94 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. C2×#17989512 | C2 | semidirect |
| 3. C2×#17989511 | C2 | semidirect |
| 5. #22624996 | C2 | semidirect |
| 6. #22624996 | C2 | semidirect |
| 23. C22⋊#11924003 | C4 | semidirect |
| 24. #17988366 | C4 | semidirect |
| 25. #17988366 | C4 | semidirect |
| 26. C22⋊C16×C73 | C4 | semidirect |
| 187. C73 | #12930 | semidirect |
| 205. C22⋊C16 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989597 | 2 |
| C2×#17989512 | 2 |
| C2×#17989511 | 2 |
| #22625810 | 2 |
| #22624996 | 2 |
| #22611540 | 2 |
| #12930 | 73 |