Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
130 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 50 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 | #1361 |
| commutator | C2×C16 | C2×C4×C7 |
| Frattini, cosocle | C4×C16 | C22×C7 |
| prime radical | C2×C7×D16 | C4 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C2×C4×C7 ◁ C4×C7×C8 ◁ C4×C7×C16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#1422 | C2 | semidirect |
| 3. C7×#1373 | C2 | semidirect |
| 11. #7447 | C7 | direct (N × H) |
| 26. #1422 | C2×C7 | semidirect |
| 27. #1373 | C2×C7 | semidirect |
| 114. C7 | #7447 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2249 | 2 |
| C7×#1422 | 2 |
| C7×#1373 | 2 |
| #7447 | 7 |