Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
230 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 230 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 |
|---|---|---|
| 1. C2×#11745176 | C2 | semidirect |
| 2. C2×#11745174 | C2 | semidirect |
| 3. #14271399 | C2 | semidirect |
| 4. #14270967 | C2 | semidirect |
| 5. #14270964 | C2 | semidirect |
| 6. C22⋊#90768 | C2 | semidirect |
| 7. C2×C29×#135 | C2 | semidirect |
| 33. Q16×C29 | D4 | semidirect |
| 36. D8×C29 | D4 | semidirect |
| 84. C2×#135 | D29 | semidirect |
| 112. C29 | #2186 | semidirect |
| 123. Q16 | C22⋊D29 | semidirect |
| 128. D8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745176 | 2 |
| C2×#11745174 | 2 |
| #14271399 | 2 |
| #14270967 | 2 |
| #14270964 | 2 |
| C22⋊#90768 | 2 |
| C2×C29×#135 | 2 |
| #2186 | 29 |