Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
310 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 10. #17989515 | C4 | semidirect |
| 11. #17989474 | C4 | semidirect |
| 15. #17988415 | C4 | semidirect |
| 16. #17988412 | C4 | semidirect |
| 17. #367×C73 | C4 | semidirect |
| 100. C73 | #12671 | semidirect |
| 109. #367 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989515 | 2 |
| C2×#17989474 | 2 |
| #22625735 | 2 |
| #22624992 | 2 |
| #22611714 | 2 |
| #12671 | 73 |