Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
820 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 253 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×#11745249 | C2 | semidirect |
| 3. #14271068 | C2 | semidirect |
| 4. #14271067 | C2 | semidirect |
| 12. C22×Dic58 | C4 | semidirect |
| 50. C22⋊Dic29 | Q8 | semidirect |
| 78. C2×Dic29 | C2×Q8 | semidirect |
| 81. Dic58 | C22⋊C4 | semidirect |
| 87. C22×C29 | C4×Q8 | semidirect |
| 133. C29 | Q8×C22⋊C4 | semidirect |
| 192. C22 | #11745249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic58 | 2 |
| C2×#11745249 | 2 |
| #14271068 | 2 |
| #14271067 | 2 |
| #14271021 | 2 |
| C22⋊C4×Dic29 | 2 |
| C4×C22⋊Dic29 | 2 |
| C29×#380 | 2 |
| Q8×C22⋊C4 | 29 |