Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
486 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 2. C2×#17989474 | C2 | semidirect |
| 4. #22624968 | C2 | semidirect |
| 7. C2×#14556664 | C4 | semidirect |
| 10. C22×#11924031 | C4 | semidirect |
| 18. C22⋊#11924003 | C4 | semidirect |
| 19. #17988366 | C4 | semidirect |
| 20. C22⋊C16×C73 | C4 | semidirect |
| 56. #11924031 | C22⋊C4 | semidirect |
| 111. C22×C73 | #346 | semidirect |
| 116. C2×D73 | #346 | semidirect |
| 138. C73 | #12611 | semidirect |
| 151. C22⋊C16 | #64408 | semidirect |
| 251. C22 | #17989474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556664 | 2 |
| C2×#17989474 | 2 |
| C8×C22⋊#64408 | 2 |
| #22624968 | 2 |
| C22⋊C16×D73 | 2 |
| #12611 | 73 |