Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
618 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 618 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, prime radical | C23×C7 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 18. #10309 | C7 | direct (N × H) |
| 68. C2×C7×C8 | Q16 | semidirect |
| 171. C2×C8 | C7×Q16 | semidirect |
| 211. C7 | #10309 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#500 | 2 |
| C2×C7×#494 | 2 |
| C7×#1990 | 2 |
| C7×#1956 | 2 |
| C7×#1273 | 2 |
| #10309 | 7 |