Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
360 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 110 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 | #1519 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C2×M16 | C23×C7 |
| prime radical | C2×C7×#41 | D4 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C2×C4×C7 ◁ C2×C7×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C7×#1342 | C2 | semidirect |
| 20. #11871 | C7 | direct (N × H) |
| 57. #1342 | C2×C7 | semidirect |
| 265. C7 | #11871 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3059 | 2 |
| C7×#2115 | 2 |
| C7×#1813 | 2 |
| C7×#1342 | 2 |
| #11871 | 7 |