Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
534 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 106 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. #17989441 | C4 | semidirect |
| 11. #17989438 | C4 | semidirect |
| 16. #17988615 | C4 | semidirect |
| 17. #17988554 | C4 | semidirect |
| 19. #17988542 | C4 | semidirect |
| 20. C2×#131×C73 | C4 | semidirect |
| 149. C73 | #8238 | semidirect |
| 150. C2×#131 | #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 |
| #22625306 | 2 |
| #22624813 | 2 |
| #22624811 | 2 |
| #22618623 | 2 |
| #8238 | 73 |