Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
384 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 165 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. #14271570 | C2 | direct (N × H) |
| 38. C2×C8×C29 | Q8 | semidirect |
| 53. C2×#6597 | Q8 | semidirect |
| 73. C8×C29 | C2×Q8 | semidirect |
| 74. #6597 | C2×Q8 | semidirect |
| 97. C2×C29 | #501 | semidirect |
| 121. C29 | C2×#501 | semidirect |
| 133. C2×C8 | Dic58 | semidirect |
| 167. C8 | C2×Dic58 | semidirect |
| 181. C2 | #14271570 | 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 |
| C2×#11745252 | 2 |
| #14271570 | 2 |
| C2×#11745166 | 2 |
| C2×#11745155 | 2 |
| C2×#11745156 | 2 |
| C2×#11745163 | 2 |
| C2×C29×#106 | 2 |
| C2×#501 | 29 |