Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
318 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 110 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. #17989514 | C4 | semidirect |
| 11. #17989513 | C4 | semidirect |
| 12. C16×#64408 | C4 | semidirect |
| 13. C16×#64408 | C4 | semidirect |
| 17. #17988417 | C4 | semidirect |
| 18. #17988416 | C4 | semidirect |
| 19. #368×C73 | C4 | semidirect |
| 107. C73 | #12670 | semidirect |
| 116. #368 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626282 | 2 |
| C2×C16×#64408 | 2 |
| #22625736 | 2 |
| #22624994 | 2 |
| #368×D73 | 2 |
| #12670 | 73 |