Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
124 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #481 |
| commutator, Frattini, cosocle | C2×C8 | C23×C7 |
| prime radical | C23×C7 | SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C2×C4×C7 ◁ C2×C7×M16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C7×#365 | C2 | semidirect |
| 4. C7×#362 | C2 | semidirect |
| 15. #2239 | C7 | direct (N × H) |
| 31. #365 | C2×C7 | semidirect |
| 32. #362 | C2×C7 | semidirect |
| 91. C7 | #2239 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#470 | 2 |
| C7×#430 | 2 |
| C7×#365 | 2 |
| C7×#362 | 2 |
| C7×#349 | 2 |
| #2239 | 7 |