Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
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×Dic142 | C2 | semidirect |
| 2. C23×#11765853 | C2 | direct (N × H) |
| 3. C24×C71⋊C8 | C2 | semidirect |
| 6. C23×Dic142 | C22 | semidirect |
| 8. C22×#11765853 | C22 | direct (N × H) |
| 9. C23×C71⋊C8 | C22 | semidirect |
| 15. C22×Dic142 | C23 | semidirect |
| 17. C2×#11765853 | C23 | direct (N × H) |
| 18. C22×C71⋊C8 | C23 | semidirect |
| 27. C2×Dic142 | C24 | semidirect |
| 29. #11765853 | C24 | direct (N × H) |
| 30. C2×C71⋊C8 | C24 | semidirect |
| 33. C24×C71 | SD16 | semidirect |
| 41. C23×C71 | C2×SD16 | semidirect |
| 49. Dic142 | C25 | semidirect |
| 50. C71⋊C8 | C25 | semidirect |
| 53. C22×C71 | C22×SD16 | semidirect |
| 60. C2×C71 | C23×SD16 | semidirect |
| 66. C71 | C24×SD16 | semidirect |
| 90. C24 | #11765853 | direct (N × H) |
| 103. C23 | C2×#11765853 | direct (N × H) |
| 115. C22 | C22×#11765853 | direct (N × H) |
| 121. C2 | C23×#11765853 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic142 | 2 |
| C23×#11765853 | 2 |
| C24×C71⋊C8 | 2 |
| C24×D4×C71 | 2 |
| C24×SD16 | 71 |