Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
322 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 96 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 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C7 |
| Frattini, cosocle | C22×C4 | C23×C7 |
| prime radical | C2×C7×#121 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#407 | C2 | semidirect |
| 3. C2×C7×C22⋊C8 | C2 | semidirect |
| 4. C7×#323 | C2 | semidirect |
| 20. #1471 | C7 | direct (N × H) |
| 46. #407 | C2×C7 | semidirect |
| 47. C2×C22⋊C8 | C2×C7 | semidirect |
| 48. #323 | C2×C7 | semidirect |
| 171. C7 | #1471 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#121 | 2 |
| C7×#407 | 2 |
| C2×C7×C22⋊C8 | 2 |
| C7×#323 | 2 |
| #1471 | 7 |