Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
426 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 215 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. C23×Dic29 | C2 | semidirect |
| 3. C2×C22⋊Dic29 | C2 | semidirect |
| 4. D4×Dic29 | C2 | direct (N × H) |
| 5. C2×C4⋊Dic29 | C2 | semidirect |
| 6. C2×C4×Dic29 | C2 | semidirect |
| 8. C2×D4×C29 | C4 | semidirect |
| 15. C22×Dic29 | C22 | semidirect |
| 16. C22⋊Dic29 | C22 | semidirect |
| 17. C4⋊Dic29 | C22 | semidirect |
| 18. C4×Dic29 | C22 | semidirect |
| 21. C23×C29 | C2×C4 | semidirect |
| 24. D4×C29 | C2×C4 | semidirect |
| 25. C2×C4×C29 | C2×C4 | semidirect |
| 30. C2×Dic29 | D4 | direct (N × H) |
| 38. C22×C29 | C22×C4 | semidirect |
| 42. C4×C29 | C22×C4 | semidirect |
| 45. Dic29 | C2×D4 | direct (N × H) |
| 48. C2×C29 | C4×D4 | semidirect |
| 58. C29 | C2×C4×D4 | semidirect |
| 60. C2×D4 | Dic29 | direct (N × H) |
| 73. C23 | C2×Dic29 | semidirect |
| 76. D4 | C2×Dic29 | direct (N × H) |
| 84. C2×C4 | C2×Dic29 | semidirect |
| 92. C22 | C22×Dic29 | semidirect |
| 97. C4 | C22×Dic29 | semidirect |
| 99. C2 | D4×Dic29 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×C29 | 2 |
| C23×Dic29 | 2 |
| C2×C22⋊Dic29 | 2 |
| D4×Dic29 | 2 |
| C2×C4⋊Dic29 | 2 |
| C2×C4×Dic29 | 2 |
| C2×C4×D4 | 29 |