Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1062 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 462 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C23×C7 | C23×C4 |
| prime radical | C24×C7 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#1839 | C2 | semidirect |
| 10. #20772 | C7 | direct (N × H) |
| 22. #1839 | C2×C7 | semidirect |
| 36. C42×C7 | M16 | semidirect |
| 83. C42 | C7×M16 | semidirect |
| 98. C7 | #20772 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C43×C7 | 2 |
| C7×#1839 | 2 |
| C7×#1728 | 2 |
| #20772 | 7 |