Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
908 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 277 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. #14271083 | C2 | direct (N × H) |
| 28. C22×C4×C29 | Q8 | semidirect |
| 37. C22×Dic29 | Q8 | semidirect |
| 60. C2×C4×C29 | C2×Q8 | semidirect |
| 68. C2×Dic29 | C2×Q8 | semidirect |
| 92. C2×C29 | #395 | semidirect |
| 112. C29 | C2×#395 | semidirect |
| 130. C22×C4 | Dic58 | semidirect |
| 160. C2×C4 | C2×Dic58 | semidirect |
| 177. C2 | #14271083 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic58 | 2 |
| C22×#90779 | 2 |
| #14271083 | 2 |
| C2×#11745179 | 2 |
| C22×C4⋊C4×C29 | 2 |
| C2×#395 | 29 |