Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
762 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 11. #17989458 | C4 | semidirect |
| 16. #17988457 | C4 | semidirect |
| 17. #17988452 | C4 | semidirect |
| 18. #17988452 | C4 | semidirect |
| 21. #384×C73 | C4 | semidirect |
| 63. #11924038 | C4⋊C4 | semidirect |
| 188. C73 | #10893 | semidirect |
| 197. #384 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626497 | 2 |
| #22625631 | 2 |
| #22625610 | 2 |
| C2×#17989458 | 2 |
| #22612336 | 2 |
| #10893 | 73 |