Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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⋊C4×D29 | C2 | semidirect |
| 3. C2×#11745169 | C2 | semidirect |
| 4. C2×#11745157 | C2 | semidirect |
| 5. C2×#11745168 | C2 | semidirect |
| 6. #14270925 | C2 | semidirect |
| 7. C29×#340 | C2 | semidirect |
| 20. #11745257 | C4 | semidirect |
| 41. C2×D116 | C2×C4 | semidirect |
| 56. C4⋊C4×C29 | C2×C4 | semidirect |
| 57. C4⋊C4×C29 | D4 | semidirect |
| 60. C4⋊Dic29 | D4 | semidirect |
| 131. C2×D29 | #102 | semidirect |
| 146. #340 | D29 | semidirect |
| 174. C29 | #1874 | semidirect |
| 211. C4⋊C4 | C4×D29 | semidirect |
| 212. C4⋊C4 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745257 | 2 |
| C2×C4⋊C4×D29 | 2 |
| C2×#11745169 | 2 |
| C2×#11745157 | 2 |
| C2×#11745168 | 2 |
| #14270925 | 2 |
| C29×#340 | 2 |
| #1874 | 29 |