Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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. #14271637 | C2 | semidirect |
| 3. #14271181 | C2 | semidirect |
| 4. #14271167 | C2 | semidirect |
| 5. #14271136 | C2 | semidirect |
| 6. #14270934 | C2 | semidirect |
| 7. C29×H(3,ℤ/4) | C2 | semidirect |
| 17. C2×D232 | C4 | semidirect |
| 18. C2×#90773 | C4 | semidirect |
| 36. C2×D116 | C2×C4 | semidirect |
| 41. C2×Dic58 | C2×C4 | semidirect |
| 44. C2×C8×C29 | C2×C4 | semidirect |
| 116. H(3,ℤ/4) | D29 | semidirect |
| 140. C29 | #1904 | semidirect |
| 165. C2×C8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745270 | 2 |
| #14271637 | 2 |
| #14271181 | 2 |
| #14271167 | 2 |
| #14271136 | 2 |
| #14270934 | 2 |
| C29×H(3,ℤ/4) | 2 |
| #1904 | 29 |