Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
5796 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | C26 |
| commutator, Frattini, cosocle | C2 | C26×C7 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#585 | C2 | semidirect |
| 2. C2×C7×2−1+4 | C2 | semidirect |
| 3. C7×2−1+4 | C22 | semidirect |
| 4. C7×H(5,𝔽2) | C22 | semidirect |
| 5. C2×C7×#41 | C22 | semidirect |
| 6. C22×C7×Q8 | C22 | semidirect |
| 7. 2−1+6 | C7 | direct (N × H) |
| 12. #585 | C2×C7 | semidirect |
| 13. C2×2−1+4 | C2×C7 | semidirect |
| 18. 2−1+4 | C22×C7 | semidirect |
| 19. H(5,𝔽2) | C22×C7 | semidirect |
| 20. C2×#41 | C22×C7 | semidirect |
| 21. C22×Q8 | C22×C7 | semidirect |
| 35. C7 | 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 |
|---|---|
| C7×#585 | 2 |
| C2×C7×2−1+4 | 2 |
| 2−1+6 | 7 |