Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
310 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 310 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 | C4×C29 | #120 |
| commutator | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×C4 | C23×C29 |
| socle | C2×C29 | #386 |
| prime radical | C29×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×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×#416 | C2 | semidirect |
| 5. C29×#408 | C2 | semidirect |
| 6. C29×#344 | C2 | semidirect |
| 7. C29×#341 | C2 | semidirect |
| 11. C29×#137 | C4 | semidirect |
| 13. C29×AGL(1,ℤ/8) | C4 | semidirect |
| 97. #1881 | C29 | direct (N × H) |
| 114. #568 | C2×C29 | semidirect |
| 115. #421 | C2×C29 | semidirect |
| 116. #416 | C2×C29 | semidirect |
| 117. #408 | C2×C29 | semidirect |
| 118. #344 | C2×C29 | semidirect |
| 119. #341 | C2×C29 | semidirect |
| 129. #137 | C4×C29 | semidirect |
| 131. AGL(1,ℤ/8) | C4×C29 | semidirect |
| 145. C29 | #1881 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#575 | 2 |
| C29×#568 | 2 |
| C29×#421 | 2 |
| C29×#416 | 2 |
| C29×#408 | 2 |
| C29×#344 | 2 |
| C29×#341 | 2 |
| #1881 | 29 |