Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
510 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 64 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. C2×#17989493 | C2 | semidirect |
| 2. C2×#17989443 | C2 | semidirect |
| 3. #22625054 | C2 | direct (N × H) |
| 8. #17989493 | C22 | semidirect |
| 10. #17989443 | C22 | semidirect |
| 15. #17988760 | C4 | semidirect |
| 18. C2×#14556510 | C4 | semidirect |
| 19. C2×2−1+4×C73 | C4 | semidirect |
| 43. #14556510 | C2×C4 | semidirect |
| 47. 2−1+4×C73 | C2×C4 | semidirect |
| 174. C2×C73 | #1404 | semidirect |
| 182. C73 | C2×#1404 | semidirect |
| 183. C2×2−1+4 | #64408 | semidirect |
| 201. 2−1+4 | C2×#64408 | semidirect |
| 353. C2 | #22625054 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989493 | 2 |
| C2×#17989443 | 2 |
| #22625054 | 2 |
| C2×#17988760 | 2 |
| C2×#1404 | 73 |