Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
652 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 217 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. C2×#11745234 | C2 | semidirect |
| 4. #14271059 | C2 | semidirect |
| 5. #14271052 | C2 | semidirect |
| 6. C4×#90781 | C2 | semidirect |
| 7. C42×Dic29 | C2 | semidirect |
| 8. C4×C4⋊C4×C29 | C2 | semidirect |
| 23. C4×D116 | C4 | semidirect |
| 51. C4×Dic29 | D4 | semidirect |
| 92. C4×C29 | #117 | semidirect |
| 102. C4×C4⋊C4 | D29 | semidirect |
| 129. C29 | #2293 | semidirect |
| 197. C4 | #11745234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D116 | 2 |
| C2×#11745234 | 2 |
| #14271064 | 2 |
| #14271059 | 2 |
| #14271052 | 2 |
| C4×#90781 | 2 |
| C42×Dic29 | 2 |
| C4×C4⋊C4×C29 | 2 |
| #2293 | 29 |