Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
264 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 84 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 | #99 |
| commutator | C23 | C22×C4×C29 |
| Frattini, cosocle | C2×D4 | C23×C29 |
| socle | C2×C29 | C2×#99 |
| prime radical | C29×#525 | C2 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C2×C4×C29 ◁ C2×#41×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#413 | C2 | semidirect |
| 3. C29×#410 | C2 | semidirect |
| 4. C29×#352 | C2 | semidirect |
| 5. C29×AΣL(1,𝔽16) | C2 | semidirect |
| 7. C23×C4×C29 | C4 | semidirect |
| 9. C29×#123 | C4 | semidirect |
| 13. C29×#120 | C4 | semidirect |
| 18. C29×#117 | C4 | semidirect |
| 87. #2120 | C29 | direct (N × H) |
| 110. #413 | C2×C29 | semidirect |
| 111. #410 | C2×C29 | semidirect |
| 112. #352 | C2×C29 | semidirect |
| 113. AΣL(1,𝔽16) | C2×C29 | semidirect |
| 121. C23×C4 | C4×C29 | semidirect |
| 123. #123 | C4×C29 | semidirect |
| 127. #120 | C4×C29 | semidirect |
| 132. #117 | C4×C29 | semidirect |
| 137. C29 | #2120 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#525 | 2 |
| C29×#413 | 2 |
| C29×#410 | 2 |
| C29×#352 | 2 |
| C29×AΣL(1,𝔽16) | 2 |
| #2120 | 29 |