Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
540 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 540 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 |
|---|---|---|
| 15. #17989447 | C4 | semidirect |
| 18. #17988336 | C4 | semidirect |
| 19. #17988335 | C4 | semidirect |
| 20. #333×C73 | C4 | semidirect |
| 120. #64408 | #333 | direct (N × H) |
| 140. C73 | C4×#333 | semidirect |
| 155. #333 | #64408 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×#64408 | 2 |
| C4⋊C8×#64408 | 2 |
| D73⋊#333 | 2 |
| #22624810 | 2 |
| #333×D73 | 2 |
| C4×#333 | 73 |