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. #17988340 | C4 | semidirect |
| 18. #17988339 | C4 | semidirect |
| 19. #335×C73 | C4 | semidirect |
| 100. C8×C73 | #107 | semidirect |
| 103. #10596831 | #107 | semidirect |
| 131. C73 | #9617 | semidirect |
| 145. #335 | #64408 | semidirect |
| 229. C8 | #14556660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626042 | 2 |
| #22625866 | 2 |
| #22625725 | 2 |
| #22624810 | 2 |
| #335×D73 | 2 |
| #9617 | 73 |