Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
572 conjugacy classes of subgroups.
The subgroup lattice has 108 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C4×C8×C29 | C22 |
| commutator | C2 | C22×C42×C29 |
| Frattini, cosocle | C2×C4 | C24×C29 |
| socle | C22×C29 | C23×C4 |
| prime radical | C2×#41×C29 | C22 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C29×#405 | C2 | semidirect |
| 4. C4×M16×C29 | C2 | semidirect |
| 5. C2×C4×C8×C29 | C2 | semidirect |
| 7. C29×#131 | C4 | direct (N × H) |
| 23. M16×C29 | C2×C4 | semidirect |
| 24. C2×C8×C29 | C2×C4 | semidirect |
| 43. C4×#131 | C29 | direct (N × H) |
| 49. C4×C29 | #131 | direct (N × H) |
| 53. #405 | C2×C29 | semidirect |
| 54. C4×M16 | C2×C29 | semidirect |
| 55. C2×C4×C8 | C2×C29 | semidirect |
| 60. #131 | C4×C29 | direct (N × H) |
| 71. C29 | C4×#131 | direct (N × H) |
| 77. M16 | C2×C4×C29 | semidirect |
| 78. C2×C8 | C2×C4×C29 | semidirect |
| 102. C4 | C29×#131 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#131 | 2 |
| C4×#41×C29 | 2 |
| C29×#405 | 2 |
| C4×M16×C29 | 2 |
| C2×C4×C8×C29 | 2 |
| C4×#131 | 29 |