Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
446 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 26. #17988883 | C4 | semidirect |
| 27. #17988882 | C4 | semidirect |
| 28. #17988869 | C4 | semidirect |
| 32. #475×C73 | C4 | semidirect |
| 211. C73 | #9178 | semidirect |
| 219. #475 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626451 | 2 |
| #22625363 | 2 |
| #22625315 | 2 |
| #22625234 | 2 |
| #22624827 | 2 |
| #22624786 | 2 |
| #22619731 | 2 |
| #9178 | 73 |