Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
174 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 55 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×#11745174 | C2 | semidirect |
| 2. C22×#90768 | C2 | semidirect |
| 3. #14271399 | C2 | semidirect |
| 4. #14270988 | C2 | semidirect |
| 5. #14270964 | C2 | semidirect |
| 6. #14270963 | C2 | semidirect |
| 7. C29×#466 | C2 | semidirect |
| 39. #90768 | D4 | semidirect |
| 64. C22×C29 | D16 | semidirect |
| 77. #466 | D29 | semidirect |
| 100. C29 | #2215 | semidirect |
| 146. C22 | #11745174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745174 | 2 |
| C22×#90768 | 2 |
| #14271399 | 2 |
| #14270988 | 2 |
| #14270964 | 2 |
| #14270963 | 2 |
| C29×#466 | 2 |
| #2215 | 29 |