Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
474 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 1. C2×#17989492 | C2 | semidirect |
| 2. #22625064 | C2 | semidirect |
| 3. #22625062 | C2 | semidirect |
| 11. #17988963 | C4 | semidirect |
| 13. #17988961 | C4 | semidirect |
| 15. C4×#11924012 | C4 | semidirect |
| 16. #532×C73 | C4 | semidirect |
| 34. C4×#10596831 | C2×C4 | semidirect |
| 35. C4×#10596831 | C2×C4 | semidirect |
| 37. C4⋊Q8×C73 | C2×C4 | semidirect |
| 38. #127×C73 | C2×C4 | semidirect |
| 135. C73 | #13584 | semidirect |
| 137. #532 | #64408 | semidirect |
| 158. C4⋊Q8 | C2×#64408 | semidirect |
| 163. #127 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989492 | 2 |
| #22625064 | 2 |
| #22625062 | 2 |
| #22620384 | 2 |
| #13584 | 73 |