Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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×#11745176 | C2 | semidirect |
| 3. #14270963 | C2 | semidirect |
| 4. C22⋊#90768 | C2 | semidirect |
| 5. C29×#467 | C2 | semidirect |
| 7. C2×Q16×C29 | C22 | semidirect |
| 13. C29×#107 | C22 | semidirect |
| 16. C2×#90768 | C22 | semidirect |
| 56. C22×C29 | SD32 | semidirect |
| 69. #467 | D29 | semidirect |
| 78. C2×Q16 | C2×D29 | semidirect |
| 86. #107 | C2×D29 | semidirect |
| 88. C29 | #2187 | semidirect |
| 131. C22 | #11745176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D232 | 2 |
| C2×#11745176 | 2 |
| #14270963 | 2 |
| C22⋊#90768 | 2 |
| C29×#467 | 2 |
| #2187 | 29 |