Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
424 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 181 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. #14271567 | C2 | direct (N × H) |
| 27. C2×C8×C29 | Q8 | semidirect |
| 36. C2×#6597 | Q8 | semidirect |
| 52. C8×C29 | C2×Q8 | semidirect |
| 53. #6597 | C2×Q8 | semidirect |
| 72. C2×C29 | #500 | semidirect |
| 89. C29 | C2×#500 | semidirect |
| 99. C2×C8 | Dic58 | semidirect |
| 123. C8 | C2×Dic58 | semidirect |
| 135. C2 | #14271567 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745250 | 2 |
| #14271567 | 2 |
| C2×#11745166 | 2 |
| C2×#11745155 | 2 |
| C2×C8×Dic29 | 2 |
| C2×C29×#107 | 2 |
| C2×#500 | 29 |