Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
352 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 5. C2×#14556659 | C4 | semidirect |
| 9. #17989461 | C4 | semidirect |
| 12. C22⋊#11924003 | C4 | semidirect |
| 14. C22⋊C16×C73 | C4 | semidirect |
| 122. C73 | #7262 | semidirect |
| 130. C22⋊C16 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625807 | 2 |
| #22625617 | 2 |
| #22611540 | 2 |
| #7262 | 73 |