Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
618 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 105 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×#11745153 | C2 | semidirect |
| 3. #14271127 | C2 | semidirect |
| 4. C4×C22⋊C4×C29 | C2 | semidirect |
| 10. C2×#90805 | C4 | semidirect |
| 12. C22×D116 | C4 | semidirect |
| 14. C22×Dic58 | C4 | semidirect |
| 16. C2×C42×C29 | C22 | semidirect |
| 17. C2×#90777 | C22 | semidirect |
| 84. D116 | C22⋊C4 | semidirect |
| 89. Dic58 | C22⋊C4 | semidirect |
| 100. C22×C29 | #104 | semidirect |
| 116. C4×C22⋊C4 | D29 | semidirect |
| 136. C2×C42 | C2×D29 | semidirect |
| 141. C29 | #1789 | semidirect |
| 223. C22 | #11745153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90805 | 2 |
| C2×#11745153 | 2 |
| #14271127 | 2 |
| C4×C22⋊C4×C29 | 2 |
| #1789 | 29 |