Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
320 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 125 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. C4×#90777 | C2 | semidirect |
| 3. #14271009 | C2 | semidirect |
| 4. #14270922 | C2 | semidirect |
| 7. C4×Q8×C29 | C4 | semidirect |
| 9. C4×D4×C29 | C4 | semidirect |
| 16. #11745185 | C4 | semidirect |
| 40. C4×Dic29 | C2×C4 | semidirect |
| 42. #90777 | C2×C4 | semidirect |
| 90. C4×Q8 | Dic29 | semidirect |
| 92. C4×D4 | Dic29 | semidirect |
| 102. C29 | #1759 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745185 | 2 |
| C4×#90777 | 2 |
| #14271009 | 2 |
| #14270922 | 2 |
| C4×#41×C29 | 2 |
| #1759 | 29 |