Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
13310 conjugacy classes of subgroups; only the 4427 normal subgroups are shown.
This group has 13310 conjugacy classes of subgroups — too many to draw. Only its 4427 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. C24×Dic146 | C2 | semidirect |
| 2. C23×#11924016 | C2 | direct (N × H) |
| 3. C24×#10596831 | C2 | semidirect |
| 6. C23×Dic146 | C22 | semidirect |
| 8. C22×#11924016 | C22 | direct (N × H) |
| 9. C23×#10596831 | C22 | semidirect |
| 15. C22×Dic146 | C23 | semidirect |
| 17. C2×#11924016 | C23 | direct (N × H) |
| 18. C22×#10596831 | C23 | semidirect |
| 27. C2×Dic146 | C24 | semidirect |
| 29. #11924016 | C24 | direct (N × H) |
| 30. C2×#10596831 | C24 | semidirect |
| 33. C24×C73 | SD16 | semidirect |
| 41. C23×C73 | C2×SD16 | semidirect |
| 49. Dic146 | C25 | semidirect |
| 50. #10596831 | C25 | semidirect |
| 53. C22×C73 | C22×SD16 | semidirect |
| 60. C2×C73 | C23×SD16 | semidirect |
| 66. C73 | C24×SD16 | semidirect |
| 90. C24 | #11924016 | direct (N × H) |
| 103. C23 | C2×#11924016 | direct (N × H) |
| 115. C22 | C22×#11924016 | direct (N × H) |
| 121. C2 | C23×#11924016 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic146 | 2 |
| C23×#11924016 | 2 |
| C24×#10596831 | 2 |
| C24×D4×C73 | 2 |
| C24×SD16 | 73 |