Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
314 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 10. #17989516 | C4 | semidirect |
| 11. #17989515 | C4 | semidirect |
| 17. #17988417 | C4 | semidirect |
| 18. #17988416 | C4 | semidirect |
| 19. #368×C73 | C4 | semidirect |
| 92. #64408 | #368 | direct (N × H) |
| 107. C73 | C4×#368 | semidirect |
| 118. #368 | #64408 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D73⋊#368 | 2 |
| C2×C16×#64408 | 2 |
| #108×#64408 | 2 |
| #22624990 | 2 |
| #368×D73 | 2 |
| C4×#368 | 73 |