Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
924 conjugacy classes of subgroups; only the 368 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 368 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C29 | C23 |
| commutator | C22 | C23×C4×C29 |
| Frattini, cosocle | C23 | C24×C29 |
| socle | C23×C29 | C24 |
| prime radical | C2×C29×#127 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×D4×C29 | C2 | semidirect |
| 3. C29×#390 | C2 | semidirect |
| 4. C29×#384 | C2 | semidirect |
| 5. C43×C29 | C2 | semidirect |
| 8. C29×#127 | C4 | direct (N × H) |
| 18. C2×D4×C29 | C2×C4 | semidirect |
| 27. C42×C29 | C2×C4 | semidirect |
| 28. C42×C29 | D4 | semidirect |
| 42. C4×#127 | C29 | direct (N × H) |
| 51. C4×C29 | C4×D4 | semidirect |
| 52. C4×C29 | #127 | direct (N × H) |
| 54. C2×C4×D4 | C2×C29 | semidirect |
| 55. #390 | C2×C29 | semidirect |
| 56. #384 | C2×C29 | semidirect |
| 57. C43 | C2×C29 | semidirect |
| 64. #127 | C4×C29 | direct (N × H) |
| 71. C29 | C4×#127 | direct (N × H) |
| 75. C2×D4 | C2×C4×C29 | semidirect |
| 84. C42 | C2×C4×C29 | semidirect |
| 85. C42 | D4×C29 | semidirect |
| 107. C4 | C4×D4×C29 | semidirect |
| 108. C4 | C29×#127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#127 | 2 |
| C2×C4×D4×C29 | 2 |
| C29×#390 | 2 |
| C29×#384 | 2 |
| C43×C29 | 2 |
| C4×#127 | 29 |