Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
216 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 92 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 | #121 |
| commutator | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×C4 | C23×C29 |
| socle | C2×C29 | #388 |
| prime radical | C2×#41×C29 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C22×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#430 | C2 | semidirect |
| 5. C4×M16×C29 | C2 | semidirect |
| 6. C29×#344 | C2 | semidirect |
| 7. C29×#339 | C2 | semidirect |
| 19. C29×#101 | C4 | semidirect |
| 20. C29×#100 | C4 | semidirect |
| 76. #1932 | C29 | direct (N × H) |
| 91. #430 | C2×C29 | semidirect |
| 95. C4×M16 | C2×C29 | semidirect |
| 96. #344 | C2×C29 | semidirect |
| 97. #339 | C2×C29 | semidirect |
| 114. #101 | C4×C29 | semidirect |
| 115. #100 | C4×C29 | semidirect |
| 118. C29 | #1932 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#430 | 2 |
| C29×#421 | 2 |
| C2×C29×#104 | 2 |
| C29×#413 | 2 |
| C4×M16×C29 | 2 |
| C29×#344 | 2 |
| C29×#339 | 2 |
| #1932 | 29 |