Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C29 | C22⋊C4 |
| commutator | C22 | C2×C42×C29 |
| Frattini, cosocle | C22×C4 | C23×C29 |
| socle | C22×C29 | C2×C22⋊C4 |
| prime radical | C22×D4×C29 | C22 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×M16×C29 | C2 | semidirect |
| 4. C29×#343 | C2 | semidirect |
| 13. C29×#100 | C4 | direct (N × H) |
| 28. M16×C29 | C2×C4 | semidirect |
| 54. C4×#100 | C29 | direct (N × H) |
| 68. C4×C29 | #100 | direct (N × H) |
| 72. C4×M16 | C2×C29 | semidirect |
| 73. #343 | C2×C29 | semidirect |
| 88. #100 | C4×C29 | direct (N × H) |
| 91. C29 | C4×#100 | direct (N × H) |
| 104. M16 | C2×C4×C29 | semidirect |
| 143. C4 | C29×#100 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C29 | 2 |
| C2×C29×#100 | 2 |
| C4×M16×C29 | 2 |
| C29×#343 | 2 |
| C4×#100 | 29 |