Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
740 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×D116 | C2 | semidirect |
| 3. #14271065 | C2 | semidirect |
| 4. #14271041 | C2 | semidirect |
| 5. #14271029 | C2 | semidirect |
| 6. C29×#376 | C2 | semidirect |
| 16. #11745236 | C4 | semidirect |
| 29. C2×D116 | C2×C4 | semidirect |
| 30. C2×D116 | C2×C4 | semidirect |
| 34. C42×C29 | C2×C4 | semidirect |
| 35. C42×C29 | D4 | semidirect |
| 79. #376 | D29 | semidirect |
| 98. C29 | #2328 | semidirect |
| 116. C42 | C4×D29 | semidirect |
| 117. C42 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745236 | 2 |
| C2×C4×D116 | 2 |
| #14271065 | 2 |
| #14271041 | 2 |
| #14271029 | 2 |
| C29×#376 | 2 |
| #2328 | 29 |