Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
658 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 8. #17989455 | C4 | semidirect |
| 13. C2×#14556501 | C4 | semidirect |
| 14. C2×C4×#10596831 | C4 | semidirect |
| 15. C2×C8×Dic73 | C4 | semidirect |
| 16. C2×#97×C73 | C4 | semidirect |
| 137. C73 | #10814 | semidirect |
| 144. C2×#97 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625630 | 2 |
| #22625617 | 2 |
| C2×#17989455 | 2 |
| C2×#17988544 | 2 |
| #10814 | 73 |