Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
5796 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | C26 |
| commutator, Frattini, cosocle | C2 | C26×C29 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#585 | C2 | semidirect |
| 2. C2×C29×2−1+4 | C2 | semidirect |
| 3. C29×2−1+4 | C22 | semidirect |
| 4. C29×H(5,𝔽2) | C22 | semidirect |
| 5. C2×#41×C29 | C22 | semidirect |
| 6. C22×Q8×C29 | C22 | semidirect |
| 15. 2−1+6 | C29 | direct (N × H) |
| 19. #585 | C2×C29 | semidirect |
| 20. C2×2−1+4 | C2×C29 | semidirect |
| 23. 2−1+4 | C22×C29 | semidirect |
| 24. H(5,𝔽2) | C22×C29 | semidirect |
| 25. C2×#41 | C22×C29 | semidirect |
| 26. C22×Q8 | C22×C29 | semidirect |
| 27. C29 | 2−1+6 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#585 | 2 |
| C2×C29×2−1+4 | 2 |
| 2−1+6 | 29 |