Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
594 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 186 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 | #2842 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#2091 | C2 | semidirect |
| 2. C7×#2070 | C2 | semidirect |
| 3. C7×#2069 | C2 | semidirect |
| 11. #32877 | C7 | direct (N × H) |
| 23. #2091 | C2×C7 | semidirect |
| 24. #2070 | C2×C7 | semidirect |
| 25. #2069 | C2×C7 | semidirect |
| 113. C7 | #32877 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2091 | 2 |
| C7×#2070 | 2 |
| C7×#2069 | 2 |
| C7×#1785 | 2 |
| #32877 | 7 |