Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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 |
|---|---|---|
| 1. #14271775 | C2 | direct (N × H) |
| 2. C2×#11745231 | C2 | semidirect |
| 4. C2×#11745232 | C2 | semidirect |
| 5. C2×#11745251 | C2 | semidirect |
| 7. C2×C4×Dic58 | C2 | semidirect |
| 24. #11745251 | C22 | semidirect |
| 26. #11745232 | C22 | semidirect |
| 27. #11745231 | C22 | semidirect |
| 28. C4×Dic58 | C22 | semidirect |
| 91. C2×C29 | #541 | semidirect |
| 114. C29 | C2×#541 | semidirect |
| 168. C2 | #14271775 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271775 | 2 |
| C2×#11745231 | 2 |
| C2×#11745241 | 2 |
| C2×#11745232 | 2 |
| C2×#11745251 | 2 |
| C2×#11745286 | 2 |
| C2×C4×Dic58 | 2 |
| C2×C29×#117 | 2 |
| C2×#541 | 29 |