Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
370 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | #120 |
| 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 ◁ C22×C29 ◁ C22×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#520 | C2 | semidirect |
| 3. C2×C29×#104 | C2 | semidirect |
| 4. C29×#418 | C2 | semidirect |
| 5. C29×#390 | C2 | semidirect |
| 6. C29×#343 | C2 | semidirect |
| 7. C29×#339 | C2 | semidirect |
| 11. C29×AGL(1,ℤ/8) | C4 | semidirect |
| 40. C2×D4×C29 | C2×C4 | semidirect |
| 52. M16×C29 | C2×C4 | semidirect |
| 75. Q8×C29 | C22⋊C4 | semidirect |
| 83. D4×C29 | C22⋊C4 | semidirect |
| 103. #1883 | C29 | direct (N × H) |
| 127. #520 | C2×C29 | semidirect |
| 128. C2×#104 | C2×C29 | semidirect |
| 129. #418 | C2×C29 | semidirect |
| 130. #390 | C2×C29 | semidirect |
| 131. #343 | C2×C29 | semidirect |
| 132. #339 | C2×C29 | semidirect |
| 143. AGL(1,ℤ/8) | C4×C29 | semidirect |
| 160. C29 | #1883 | direct (N × H) |
| 173. C2×D4 | C2×C4×C29 | semidirect |
| 185. M16 | C2×C4×C29 | semidirect |
| 208. Q8 | C22⋊C4×C29 | semidirect |
| 216. D4 | C22⋊C4×C29 | semidirect |
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×#520 | 2 |
| C2×C29×#104 | 2 |
| C29×#418 | 2 |
| C29×#390 | 2 |
| C29×#343 | 2 |
| C29×#339 | 2 |
| #1883 | 29 |