Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
258 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 92 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. #17989480 | C4 | semidirect |
| 9. #17989479 | C4 | semidirect |
| 16. #17988363 | C4 | semidirect |
| 17. #17988362 | C4 | semidirect |
| 18. C16×Dic73 | C4 | semidirect |
| 19. C4×C16×C73 | C4 | semidirect |
| 95. C73 | #12597 | semidirect |
| 106. C4×C16 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626153 | 2 |
| #22625652 | 2 |
| #22624984 | 2 |
| #22624980 | 2 |
| #22611526 | 2 |
| #12597 | 73 |