Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
320 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #14271009 | C2 | semidirect |
| 4. #14270924 | C2 | semidirect |
| 5. C4×M16×C29 | C2 | semidirect |
| 12. C4×D116 | C4 | semidirect |
| 15. C4×Dic58 | C4 | semidirect |
| 19. #11745173 | C4 | semidirect |
| 31. M16×C29 | C2×C4 | semidirect |
| 43. C4×Dic29 | C2×C4 | semidirect |
| 81. C4×M16 | D29 | semidirect |
| 102. C29 | #1759 | semidirect |
| 114. M16 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#90805 | 2 |
| C2×#11745173 | 2 |
| #14271009 | 2 |
| #14270924 | 2 |
| C4×M16×C29 | 2 |
| #1759 | 29 |