Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
354 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #427 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C22×C8 | C23×C7 |
| socle | C2×C7 | #1808 |
| prime radical | C2×C7×#41 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C2×C7×M16 ◁ C2×C7×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C7×#368 | C2 | semidirect |
| 4. C7×#1385 | C2 | semidirect |
| 15. #12840 | C7 | direct (N × H) |
| 36. C2×#368 | C2×C7 | semidirect |
| 38. #1385 | C2×C7 | semidirect |
| 159. C7 | #12840 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#504 | 2 |
| C2×C7×#368 | 2 |
| C7×#1813 | 2 |
| C7×#1385 | 2 |
| #12840 | 7 |