Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
246 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C22⋊C4 |
| commutator | C2×C4 | C42×C7 |
| Frattini, cosocle | C23×C4 | C22×C7 |
| socle | C22×C7 | #95 |
| prime radical | C24×C7 | D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C23×C4×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×C7×M16 | C4 | semidirect |
| 8. C7×#95 | C4 | semidirect |
| 9. #1297 | C7 | direct (N × H) |
| 39. C2×M16 | C4×C7 | semidirect |
| 43. #95 | C4×C7 | semidirect |
| 85. C7 | #1297 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#407 | 2 |
| C4×C7×C22⋊C4 | 2 |
| #1297 | 7 |