Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
474 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 474 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 |
|---|---|---|
| 1. C22×#90784 | C2 | semidirect |
| 3. C2×#11745157 | C2 | semidirect |
| 4. #14270918 | C2 | semidirect |
| 5. C29×#391 | C2 | semidirect |
| 22. C2×Q8×C29 | D4 | semidirect |
| 41. C2×#6597 | D4 | semidirect |
| 57. C2×C4×C29 | SD16 | semidirect |
| 87. #391 | D29 | semidirect |
| 107. C29 | #2014 | semidirect |
| 112. C2×Q8 | D116 | semidirect |
| 152. C2×C4 | #90784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90784 | 2 |
| C2×#11745236 | 2 |
| C2×#11745157 | 2 |
| #14270918 | 2 |
| C29×#391 | 2 |
| #2014 | 29 |