Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
924 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 381 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×C42×D29 | C2 | semidirect |
| 3. C4×#90779 | C2 | semidirect |
| 4. C4×#90781 | C2 | semidirect |
| 5. C4×C22⋊Dic29 | C2 | semidirect |
| 6. C42×Dic29 | C2 | semidirect |
| 7. C22×C42×C29 | C2 | semidirect |
| 15. C4×C22⋊D29 | C4 | direct (N × H) |
| 27. C22×C4×C29 | C2×C4 | semidirect |
| 36. C2×C4×D29 | C2×C4 | semidirect |
| 38. C42×C29 | D4 | semidirect |
| 39. C22⋊Dic29 | C2×C4 | semidirect |
| 40. #90781 | C2×C4 | semidirect |
| 41. #90779 | C2×C4 | semidirect |
| 44. C4×Dic29 | C2×C4 | semidirect |
| 59. C22⋊D29 | C42 | direct (N × H) |
| 70. C22×C29 | C2×C42 | semidirect |
| 76. C2×D29 | C2×C42 | semidirect |
| 78. C4×C29 | C4×D4 | semidirect |
| 81. Dic29 | C2×C42 | semidirect |
| 84. C22×C42 | D29 | semidirect |
| 109. C29 | C42×D4 | semidirect |
| 121. C22×C4 | C4×D29 | semidirect |
| 131. C42 | C22⋊D29 | direct (N × H) |
| 159. C22 | C42×D29 | semidirect |
| 167. C4 | C4×C22⋊D29 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D29 | 2 |
| C2×C42×D29 | 2 |
| C4×#90779 | 2 |
| C4×#90781 | 2 |
| C4×C22⋊Dic29 | 2 |
| C42×Dic29 | 2 |
| C22×C42×C29 | 2 |
| C42×D4 | 29 |