Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
386 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 386 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 | C23 | C22×C4×C29 |
| Frattini, cosocle | C24 | C23×C29 |
| prime radical | C22×D4×C29 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C24×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C29×#381 | C2 | semidirect |
| 5. C29×#342 | C2 | semidirect |
| 9. C29×#123 | C4 | semidirect |
| 33. C22×C4×C29 | C2×C4 | semidirect |
| 45. C22⋊C4×C29 | C2×C4 | semidirect |
| 74. #1890 | C29 | direct (N × H) |
| 97. #381 | C2×C29 | semidirect |
| 98. #342 | C2×C29 | semidirect |
| 109. #123 | C4×C29 | semidirect |
| 120. C29 | #1890 | direct (N × H) |
| 134. C22×C4 | C2×C4×C29 | semidirect |
| 146. C22⋊C4 | C2×C4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#123 | 2 |
| C29×#518 | 2 |
| C2×C29×#99 | 2 |
| C29×#381 | 2 |
| C29×#342 | 2 |
| #1890 | 29 |