Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
506 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 102 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×#17989500 | C2 | semidirect |
| 4. #22624988 | C2 | semidirect |
| 17. #17988829 | C4 | semidirect |
| 18. #17988828 | C4 | semidirect |
| 21. #17988825 | C4 | semidirect |
| 24. #467×C73 | C4 | semidirect |
| 191. C73 | #13062 | semidirect |
| 204. #467 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989643 | 2 |
| C2×#17989500 | 2 |
| #22625808 | 2 |
| #22624988 | 2 |
| #467×D73 | 2 |
| #13062 | 73 |