Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
370 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 17. #17988338 | C4 | semidirect |
| 18. #17988337 | C4 | semidirect |
| 19. #334×C73 | C4 | semidirect |
| 106. C8×C73 | #106 | semidirect |
| 109. #10596831 | #106 | semidirect |
| 141. C73 | #9621 | semidirect |
| 155. #334 | #64408 | semidirect |
| 245. C8 | #14556659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626043 | 2 |
| #22625867 | 2 |
| #22625725 | 2 |
| #22624810 | 2 |
| #334×D73 | 2 |
| #9621 | 73 |