Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
420 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 118 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×#17989478 | C2 | semidirect |
| 4. #22624971 | C2 | semidirect |
| 7. C2×#14556666 | 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 | #347 | semidirect |
| 138. C73 | #12616 | semidirect |
| 151. C22⋊C16 | #64408 | semidirect |
| 251. C22 | #17989478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556666 | 2 |
| C2×#17989478 | 2 |
| #22625667 | 2 |
| #22624971 | 2 |
| #22611540 | 2 |
| #12616 | 73 |