Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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×C42×D29 | C2 | semidirect |
| 3. C2×#11745153 | C2 | semidirect |
| 4. C2×#11745173 | C2 | semidirect |
| 5. #14271126 | C2 | semidirect |
| 6. #14270922 | C2 | semidirect |
| 7. C29×#339 | C2 | semidirect |
| 17. #11745259 | C4 | semidirect |
| 18. #11745257 | C4 | semidirect |
| 38. C2×D116 | C2×C4 | semidirect |
| 48. C2×Dic58 | C2×C4 | semidirect |
| 52. C4⋊C4×C29 | C2×C4 | semidirect |
| 56. C42×C29 | D4 | semidirect |
| 62. C4×Dic29 | D4 | semidirect |
| 114. C2×D29 | #104 | semidirect |
| 130. #339 | D29 | semidirect |
| 156. C29 | #1896 | semidirect |
| 186. C4⋊C4 | C4×D29 | semidirect |
| 195. C42 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271675 | 2 |
| C2×C42×D29 | 2 |
| C2×#11745153 | 2 |
| C2×#11745173 | 2 |
| #14271126 | 2 |
| #14270922 | 2 |
| C29×#339 | 2 |
| #1896 | 29 |