Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
382 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
| 100. C8×C73 | #107 | semidirect |
| 103. #10596831 | #107 | semidirect |
| 131. C73 | #9611 | semidirect |
| 145. #334 | #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 |
| C8×C4⋊#64408 | 2 |
| #22624810 | 2 |
| #334×D73 | 2 |
| #9611 | 73 |