Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
698 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 212 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 | C2×#120 |
| commutator, Frattini, cosocle | C2×C4 | C24×C29 |
| 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 |
|---|---|---|
| 1. C2×C29×2−1+4 | C2 | semidirect |
| 2. C29×#575 | C2 | semidirect |
| 3. C29×#536 | C2 | semidirect |
| 4. C29×#456 | C2 | semidirect |
| 5. C29×#454 | C2 | semidirect |
| 6. C29×#421 | C2 | semidirect |
| 7. C2×C29×#101 | C2 | semidirect |
| 18. C29×#137 | C22 | semidirect |
| 20. C29×AGL(1,ℤ/8) | C22 | semidirect |
| 23. C29×C4⋊Q8 | C22 | semidirect |
| 24. C29×#124 | C22 | semidirect |
| 28. C29×#104 | C22 | semidirect |
| 29. C29×#101 | C22 | semidirect |
| 103. #3020 | C29 | direct (N × H) |
| 118. C2×2−1+4 | C2×C29 | semidirect |
| 119. #575 | C2×C29 | semidirect |
| 120. #536 | C2×C29 | semidirect |
| 121. #456 | C2×C29 | semidirect |
| 122. #454 | C2×C29 | semidirect |
| 123. #421 | C2×C29 | semidirect |
| 124. C2×#101 | C2×C29 | semidirect |
| 141. #137 | C22×C29 | semidirect |
| 143. AGL(1,ℤ/8) | C22×C29 | semidirect |
| 146. C4⋊Q8 | C22×C29 | semidirect |
| 147. #124 | C22×C29 | semidirect |
| 151. #104 | C22×C29 | semidirect |
| 152. #101 | C22×C29 | semidirect |
| 153. C29 | #3020 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×2−1+4 | 2 |
| C29×#575 | 2 |
| C29×#536 | 2 |
| C29×#456 | 2 |
| C29×#454 | 2 |
| C29×#421 | 2 |
| C2×C29×#101 | 2 |
| #3020 | 29 |