Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
318 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 318 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 |
|---|---|---|
| 12. #17989476 | C4 | semidirect |
| 13. C4×#11924031 | C4 | semidirect |
| 17. C4⋊#11924003 | C4 | semidirect |
| 18. #17988405 | C4 | semidirect |
| 19. C4⋊C16×C73 | C4 | semidirect |
| 53. #11924031 | C4⋊C4 | semidirect |
| 103. C4×C73 | #347 | semidirect |
| 121. C73 | #12666 | semidirect |
| 131. C4⋊C16 | #64408 | semidirect |
| 223. C4 | #17989478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989478 | 2 |
| C4×#14556666 | 2 |
| #22625725 | 2 |
| #22624971 | 2 |
| #22611685 | 2 |
| #12666 | 73 |