Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
584 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 136 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 | C22×C4 | C23×C29 |
| prime radical | C22×#41×C29 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C29×#101 | C2 | semidirect |
| 3. C2×C29×#100 | C2 | semidirect |
| 4. C29×#407 | C2 | semidirect |
| 65. #1785 | C29 | direct (N × H) |
| 82. C2×#101 | C2×C29 | semidirect |
| 83. C2×#100 | C2×C29 | semidirect |
| 84. #407 | C2×C29 | semidirect |
| 103. C29 | #1785 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41×C29 | 2 |
| C2×C29×#101 | 2 |
| C2×C29×#100 | 2 |
| C29×#407 | 2 |
| #1785 | 29 |