Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 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. #14271716 | C2 | semidirect |
| 4. #14270934 | C2 | semidirect |
| 5. #14270924 | C2 | semidirect |
| 6. #14270919 | C2 | semidirect |
| 27. C2×Q8×C29 | Q8 | semidirect |
| 29. C2×D4×C29 | Q8 | semidirect |
| 125. C29 | #2031 | semidirect |
| 131. C2×Q8 | Dic58 | semidirect |
| 133. C2×D4 | Dic58 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271716 | 2 |
| C2×#11745185 | 2 |
| #14271137 | 2 |
| #14270934 | 2 |
| #14270924 | 2 |
| #14270919 | 2 |
| C29×#421 | 2 |
| #2031 | 29 |