Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
468 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 468 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×#17989496 | C2 | semidirect |
| 2. C2×#17989494 | C2 | semidirect |
| 3. #22625058 | C2 | direct (N × H) |
| 8. #17989496 | C22 | semidirect |
| 10. #17989494 | C22 | semidirect |
| 16. #17988974 | C4 | semidirect |
| 18. C2×#14556502 | C4 | semidirect |
| 19. C2×#127×C73 | C4 | semidirect |
| 44. #14556502 | C2×C4 | semidirect |
| 49. #127×C73 | C2×C4 | semidirect |
| 157. C2×C73 | #1406 | semidirect |
| 165. C73 | C2×#1406 | semidirect |
| 168. C2×#127 | #64408 | semidirect |
| 197. #127 | C2×#64408 | semidirect |
| 319. C2 | #22625058 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989496 | 2 |
| C2×#17989494 | 2 |
| #22625058 | 2 |
| C2×#17988974 | 2 |
| C2×#1406 | 73 |