Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 3. #14271036 | C2 | semidirect |
| 4. #14271035 | C2 | semidirect |
| 5. #14271021 | C2 | semidirect |
| 15. C2×C22⋊Dic29 | C4 | semidirect |
| 20. C2×#90779 | C22 | semidirect |
| 21. #11745179 | C22 | semidirect |
| 35. C22×Dic29 | C2×C4 | semidirect |
| 42. C22⋊Dic29 | C2×C4 | semidirect |
| 43. C22⋊Dic29 | C2×C4 | semidirect |
| 51. C23×C29 | C4⋊C4 | semidirect |
| 120. C29 | #2315 | semidirect |
| 150. C23 | #90779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic29 | 2 |
| #14271036 | 2 |
| #14271035 | 2 |
| #14271021 | 2 |
| C22×C22⋊C4×C29 | 2 |
| #2315 | 29 |