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 |
|---|---|---|
| 1. C2×#11745232 | C2 | semidirect |
| 3. #14271464 | C2 | direct (N × H) |
| 4. C2×#11745166 | C2 | semidirect |
| 5. C2×#11745165 | C2 | semidirect |
| 8. C2×C29×C4⋊C8 | C2 | semidirect |
| 23. #11745232 | C22 | semidirect |
| 24. C29×C4⋊C8 | C22 | semidirect |
| 27. #11745166 | C22 | semidirect |
| 28. #11745165 | C22 | semidirect |
| 104. C2×C4⋊C8 | D29 | semidirect |
| 107. C2×C29 | #478 | semidirect |
| 129. C4⋊C8 | C2×D29 | semidirect |
| 132. C29 | C2×#478 | semidirect |
| 203. C2 | #14271464 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745232 | 2 |
| C2×C4×D116 | 2 |
| #14271464 | 2 |
| C2×#11745166 | 2 |
| C2×#11745165 | 2 |
| C2×#11745169 | 2 |
| C2×C29×C4⋊C8 | 2 |
| C2×#478 | 29 |