Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
854 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 854 conjugacy classes of subgroups — too many to draw. Only its 144 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. #22625026 | C2 | semidirect |
| 3. #22625025 | C2 | semidirect |
| 7. #17989568 | C4 | semidirect |
| 11. C2×#14556549 | C4 | semidirect |
| 12. C2×C42×D73 | C4 | semidirect |
| 13. #17988494 | C4 | semidirect |
| 18. #391×C73 | C4 | semidirect |
| 26. #14556650 | C2×C4 | semidirect |
| 201. C73 | #12581 | semidirect |
| 211. #391 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989568 | 2 |
| #22625026 | 2 |
| #22625025 | 2 |
| #22612420 | 2 |
| #12581 | 73 |