Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
318 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 318 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. C16×#64408 | C4 | semidirect |
| 15. #17988414 | C4 | semidirect |
| 16. #17988413 | C4 | semidirect |
| 17. #366×C73 | C4 | semidirect |
| 105. C73 | #12670 | semidirect |
| 115. #366 | #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×C16×#64408 | 2 |
| #22625735 | 2 |
| #22624992 | 2 |
| #22611712 | 2 |
| #12670 | 73 |