Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D29 | C2 | semidirect |
| 3. C2×#11745153 | C2 | semidirect |
| 4. C2×#11745173 | C2 | semidirect |
| 5. C4×#90781 | C2 | semidirect |
| 6. #14270922 | C2 | semidirect |
| 7. C29×#339 | C2 | semidirect |
| 20. #11745259 | C4 | semidirect |
| 21. #11745259 | C4 | semidirect |
| 22. #11745257 | C4 | semidirect |
| 23. #11745257 | C4 | semidirect |
| 55. M16×C29 | D4 | semidirect |
| 73. #90777 | D4 | semidirect |
| 140. C2×D29 | #104 | semidirect |
| 158. #339 | D29 | semidirect |
| 190. C29 | #1871 | semidirect |
| 218. M16 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D29 | 2 |
| #14271675 | 2 |
| C2×#11745153 | 2 |
| C2×#11745173 | 2 |
| C4×#90781 | 2 |
| #14270922 | 2 |
| C29×#339 | 2 |
| #1871 | 29 |