Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
510 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. C2×#17988382 | C2 | semidirect |
| 3. #22608083 | C2 | direct (N × H) |
| 4. C2×#329×C73 | C2 | semidirect |
| 5. C2×#14556639 | C4 | semidirect |
| 9. #17988759 | C4 | semidirect |
| 12. C2×#14556510 | C4 | semidirect |
| 15. #17988382 | C22 | semidirect |
| 19. #329×C73 | C22 | semidirect |
| 23. #14556639 | C2×C4 | semidirect |
| 38. #14556510 | C2×C4 | semidirect |
| 175. C2×C73 | #1404 | semidirect |
| 180. C2×#329 | D73 | semidirect |
| 182. C73 | C2×#1404 | semidirect |
| 197. #329 | C2×D73 | semidirect |
| 353. C2 | #22608083 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988759 | 2 |
| C2×#17988382 | 2 |
| #22608083 | 2 |
| C2×#329×C73 | 2 |
| C2×#1404 | 73 |