Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
126 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #102 |
| commutator | C2×C8 | C2×C4×C7 |
| Frattini, cosocle | C22×C8 | C22×C7 |
| prime radical | C7×#466 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C22×C7×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×C22⋊C16 | C2 | semidirect |
| 3. C7×#340 | C2 | semidirect |
| 4. C2×C7×D8 | C4 | semidirect |
| 9. C7×#107 | C4 | semidirect |
| 11. #1347 | C7 | direct (N × H) |
| 26. C22⋊C16 | C2×C7 | semidirect |
| 27. #340 | C2×C7 | semidirect |
| 44. C2×D8 | C4×C7 | semidirect |
| 49. #107 | C4×C7 | semidirect |
| 99. C7 | #1347 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#466 | 2 |
| C7×C22⋊C16 | 2 |
| C7×#340 | 2 |
| #1347 | 7 |