Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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×#11745164 | C2 | semidirect |
| 3. C2×#11745169 | C2 | semidirect |
| 4. #14271023 | C2 | semidirect |
| 5. C2×C29×C22⋊C8 | C2 | semidirect |
| 11. C2×#90805 | C4 | semidirect |
| 81. D116 | C22⋊C4 | semidirect |
| 85. Dic58 | C22⋊C4 | semidirect |
| 112. C2×C22⋊C8 | D29 | semidirect |
| 137. C29 | #1788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90805 | 2 |
| C2×#11745164 | 2 |
| C2×#11745169 | 2 |
| #14271023 | 2 |
| C2×C29×C22⋊C8 | 2 |
| #1788 | 29 |