Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
630 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 12. C2×#14556591 | C4 | semidirect |
| 15. #17988492 | C4 | semidirect |
| 20. #384×C73 | C4 | semidirect |
| 180. C73 | #9683 | semidirect |
| 189. #384 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625658 | 2 |
| C2×#17989440 | 2 |
| #22625107 | 2 |
| #22618284 | 2 |
| #9683 | 73 |