Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
534 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 1. C8×C22⋊#64408 | C2 | semidirect |
| 3. #22624813 | C2 | semidirect |
| 4. #22624811 | C2 | semidirect |
| 10. #17989440 | C4 | semidirect |
| 11. #17989439 | C4 | semidirect |
| 12. C2×#14556599 | C4 | semidirect |
| 17. #17988553 | C4 | semidirect |
| 19. #17988543 | C4 | semidirect |
| 20. #424×C73 | C4 | semidirect |
| 149. C73 | #8238 | semidirect |
| 155. #424 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C22⋊#64408 | 2 |
| #22625308 | 2 |
| #22624813 | 2 |
| #22624811 | 2 |
| #22618624 | 2 |
| #8238 | 73 |