Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
438 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 103 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×C4×D116 | C2 | semidirect |
| 3. C2×#11745180 | C2 | semidirect |
| 4. C2×#11745157 | C2 | semidirect |
| 5. #14270925 | C2 | semidirect |
| 6. #14270918 | C2 | semidirect |
| 7. C29×#390 | C2 | semidirect |
| 17. C2×#90782 | C4 | semidirect |
| 33. C2×D4×C29 | C2×C4 | semidirect |
| 63. C2×#6597 | C2×C4 | semidirect |
| 91. C2×C4×C29 | D8 | semidirect |
| 104. D116 | C22⋊C4 | semidirect |
| 142. #390 | D29 | semidirect |
| 172. C29 | #1879 | semidirect |
| 186. C2×D4 | C4×D29 | semidirect |
| 246. C2×C4 | #90782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90782 | 2 |
| C2×C4×D116 | 2 |
| C2×#11745180 | 2 |
| C2×#11745157 | 2 |
| #14270925 | 2 |
| #14270918 | 2 |
| C29×#390 | 2 |
| #1879 | 29 |