Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
220 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C29 | C2×D8 |
| commutator | C8 | C22×C4×C29 |
| Frattini, cosocle | C2×C8 | C23×C29 |
| socle | C2×C29 | C2×#102 |
| prime radical | C2×C29×#135 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C22×C4×C29 ◁ C22×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C29×M32 | C2 | semidirect |
| 3. C2×C29×#108 | C2 | semidirect |
| 4. C29×#359 | C2 | semidirect |
| 17. C2×C16×C29 | C22 | semidirect |
| 19. C29×#108 | C22 | semidirect |
| 67. #2143 | C29 | direct (N × H) |
| 80. C2×M32 | C2×C29 | semidirect |
| 81. C2×#108 | C2×C29 | semidirect |
| 82. #359 | C2×C29 | semidirect |
| 100. C2×C16 | C22×C29 | semidirect |
| 102. #108 | C22×C29 | semidirect |
| 103. C29 | #2143 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#135 | 2 |
| C2×C29×M32 | 2 |
| C2×C29×#108 | 2 |
| C29×#359 | 2 |
| #2143 | 29 |