Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
448 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 157 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. #14271460 | C2 | direct (N × H) |
| 3. C2×#11745155 | C2 | semidirect |
| 4. C2×#11745156 | C2 | semidirect |
| 5. C2×C4⋊#6597 | C2 | semidirect |
| 8. C2×C29×#125 | C2 | semidirect |
| 12. C29×#125 | C22 | semidirect |
| 26. #11745156 | C22 | semidirect |
| 27. #11745155 | C22 | semidirect |
| 28. C4⋊#6597 | C22 | semidirect |
| 99. C2×#125 | D29 | semidirect |
| 107. C2×C29 | #478 | semidirect |
| 117. #125 | C2×D29 | semidirect |
| 132. C29 | C2×#478 | semidirect |
| 203. C2 | #14271460 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D116 | 2 |
| #14271460 | 2 |
| C2×#11745155 | 2 |
| C2×#11745156 | 2 |
| C2×C4⋊#6597 | 2 |
| C2×#11745157 | 2 |
| C2×C29×#125 | 2 |
| C2×#478 | 29 |