Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1664 conjugacy classes of subgroups; only the 981 normal subgroups are shown.
This group has 1664 conjugacy classes of subgroups — too many to draw. Only its 981 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×C4×Dic58 | C2 | direct (N × H) |
| 12. C22×Dic58 | C4 | direct (N × H) |
| 18. C4×Dic58 | C22 | direct (N × H) |
| 22. C22×C4×C29 | Q8 | semidirect |
| 30. C2×Dic58 | C2×C4 | direct (N × H) |
| 42. C2×C4×C29 | C2×Q8 | semidirect |
| 50. Dic58 | C22×C4 | direct (N × H) |
| 52. C22×C29 | C4×Q8 | semidirect |
| 59. C4×C29 | C22×Q8 | semidirect |
| 68. C2×C29 | C2×C4×Q8 | semidirect |
| 84. C29 | C22×C4×Q8 | semidirect |
| 93. C22×C4 | Dic58 | direct (N × H) |
| 112. C2×C4 | C2×Dic58 | direct (N × H) |
| 117. C22 | C4×Dic58 | direct (N × H) |
| 125. C4 | C22×Dic58 | direct (N × H) |
| 127. C2 | C2×C4×Dic58 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic58 | 2 |
| C2×C4×Dic58 | 2 |
| C22×C4⋊Dic29 | 2 |
| C22×#90779 | 2 |
| C22×C4×Dic29 | 2 |
| C22×C42×C29 | 2 |
| C22×C4×Q8 | 29 |