Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
226 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 226 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. C22×Dic116 | C2 | semidirect |
| 2. C2×#11745148 | C2 | semidirect |
| 4. #14270968 | C2 | semidirect |
| 5. C29×C22⋊C16 | C2 | semidirect |
| 32. Dic116 | D4 | semidirect |
| 55. C22×C29 | SD32 | semidirect |
| 69. C22⋊C16 | D29 | semidirect |
| 86. C29 | #2185 | semidirect |
| 127. C22 | #11745148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic116 | 2 |
| C2×#11745148 | 2 |
| #14271399 | 2 |
| #14270968 | 2 |
| C29×C22⋊C16 | 2 |
| #2185 | 29 |