Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
184 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C4⋊#90768 | C2 | semidirect |
| 4. #14270981 | C2 | semidirect |
| 5. C29×C4⋊C16 | C2 | semidirect |
| 40. C4×D29 | C16 | semidirect |
| 54. C4×C29 | C2×C16 | semidirect |
| 59. Dic29 | C2×C16 | semidirect |
| 64. C4⋊C16 | D29 | direct (N × H) |
| 68. D29 | C4⋊C16 | direct (N × H) |
| 79. C29 | C2×C4⋊C16 | semidirect |
| 120. C4 | C16×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D29 | 2 |
| C4×C8×D29 | 2 |
| C4⋊#90768 | 2 |
| #14270981 | 2 |
| C29×C4⋊C16 | 2 |
| C2×C4⋊C16 | 29 |