Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×Dic116 | C2 | semidirect |
| 3. #14271606 | C2 | direct (N × H) |
| 4. C2×Dic232 | C2 | semidirect |
| 5. C2×#11745148 | C2 | semidirect |
| 6. C2×C29×M32 | C2 | semidirect |
| 14. C2×Dic116 | C22 | semidirect |
| 19. C29×M32 | C22 | semidirect |
| 21. Dic232 | C22 | semidirect |
| 22. #11745148 | C22 | semidirect |
| 85. C2×M32 | D29 | semidirect |
| 87. C2×C29 | #510 | semidirect |
| 104. M32 | C2×D29 | semidirect |
| 106. C29 | C2×#510 | semidirect |
| 165. C2 | #14271606 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745266 | 2 |
| C22×Dic116 | 2 |
| #14271606 | 2 |
| C2×Dic232 | 2 |
| C2×#11745148 | 2 |
| C2×C29×M32 | 2 |
| C2×#510 | 29 |