Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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×#11745162 | C2 | semidirect |
| 5. #14270918 | C2 | semidirect |
| 6. #14270917 | C2 | semidirect |
| 7. C2×C29×C4⋊C8 | C2 | semidirect |
| 47. #90781 | C8 | semidirect |
| 70. C2×C4×C29 | C2×C8 | semidirect |
| 85. C2×Dic29 | C2×C8 | semidirect |
| 108. C2×D29 | C4⋊C8 | semidirect |
| 120. C2×C4⋊C8 | D29 | semidirect |
| 150. C29 | #1850 | semidirect |
| 209. C2×C4 | C8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D29 | 2 |
| C2×#11745162 | 2 |
| C2×#11745168 | 2 |
| C4×#90781 | 2 |
| #14270918 | 2 |
| #14270917 | 2 |
| C2×C29×C4⋊C8 | 2 |
| #1850 | 29 |