Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
634 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 16. #17988352 | C4 | semidirect |
| 17. #17988351 | C4 | semidirect |
| 18. #341×C73 | C4 | semidirect |
| 164. C73 | #11271 | semidirect |
| 175. #341 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556659 | 2 |
| C2×#17989466 | 2 |
| #22625619 | 2 |
| #22625596 | 2 |
| #341×D73 | 2 |
| #11271 | 73 |