Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
598 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 120 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 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C29 |
| Frattini, cosocle | C24 | C23×C29 |
| prime radical | C2×C29×#120 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C25×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C22⋊C4×C29 | C2 | semidirect |
| 3. C2×C29×#99 | C2 | semidirect |
| 4. C29×#379 | C2 | semidirect |
| 5. C29×#342 | C2 | semidirect |
| 7. C22×D4×C29 | C4 | semidirect |
| 16. C2×C22⋊C4×C29 | C4 | semidirect |
| 25. C24×C29 | C2×C4 | semidirect |
| 41. C22×C4×C29 | C2×C4 | semidirect |
| 42. C22×C4×C29 | C2×C4 | semidirect |
| 52. C22⋊C4×C29 | D4 | semidirect |
| 92. #1898 | C29 | direct (N × H) |
| 112. C22×C29 | #99 | semidirect |
| 123. C22×C22⋊C4 | C2×C29 | semidirect |
| 124. C2×#99 | C2×C29 | semidirect |
| 125. #379 | C2×C29 | semidirect |
| 126. #342 | C2×C29 | semidirect |
| 137. C22×D4 | C4×C29 | semidirect |
| 146. C2×C22⋊C4 | C4×C29 | semidirect |
| 151. C29 | #1898 | direct (N × H) |
| 156. C24 | C2×C4×C29 | semidirect |
| 172. C22×C4 | C2×C4×C29 | semidirect |
| 173. C22×C4 | C2×C4×C29 | semidirect |
| 183. C22⋊C4 | D4×C29 | semidirect |
| 242. C22 | C29×#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#120 | 2 |
| C22×C22⋊C4×C29 | 2 |
| C2×C29×#99 | 2 |
| C29×#379 | 2 |
| C29×#342 | 2 |
| #1898 | 29 |