Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
324 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | #386 |
| commutator | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×C4 | C23×C29 |
| prime radical | C2×C29×AGL(1,ℤ/8) | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C22×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#568 | C2 | semidirect |
| 3. C29×#421 | C2 | semidirect |
| 4. C29×#418 | C2 | semidirect |
| 5. C2×C29×#100 | C2 | semidirect |
| 6. C29×#344 | C2 | semidirect |
| 7. C29×#338 | C2 | semidirect |
| 12. C2×SD16×C29 | C4 | semidirect |
| 13. C2×D8×C29 | C4 | semidirect |
| 90. #1903 | C29 | direct (N × H) |
| 108. #568 | C2×C29 | semidirect |
| 109. #421 | C2×C29 | semidirect |
| 110. #418 | C2×C29 | semidirect |
| 111. C2×#100 | C2×C29 | semidirect |
| 112. #344 | C2×C29 | semidirect |
| 113. #338 | C2×C29 | semidirect |
| 124. C2×SD16 | C4×C29 | semidirect |
| 125. C2×D8 | C4×C29 | semidirect |
| 137. C29 | #1903 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×AGL(1,ℤ/8) | 2 |
| C29×#568 | 2 |
| C29×#421 | 2 |
| C29×#418 | 2 |
| C2×C29×#100 | 2 |
| C29×#344 | 2 |
| C29×#338 | 2 |
| #1903 | 29 |