Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
5990 conjugacy classes of subgroups; only the 750 normal subgroups are shown.
This group has 5990 conjugacy classes of subgroups — too many to draw. Only its 750 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 | C26×C7 | 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. C2×C7×#407 | C2 | semidirect |
| 3. C7×#1779 | C2 | semidirect |
| 10. C22×C7×M16 | C22 | semidirect |
| 12. C2×C7×C22⋊C8 | C22 | semidirect |
| 13. #20579 | C7 | direct (N × H) |
| 31. C22×C7×C8 | C23 | semidirect |
| 34. C2×#407 | C2×C7 | semidirect |
| 35. #1779 | C2×C7 | semidirect |
| 43. C24×C7 | M16 | semidirect |
| 70. C22×M16 | C22×C7 | semidirect |
| 72. C2×C22⋊C8 | C22×C7 | semidirect |
| 114. C22×C8 | C23×C7 | semidirect |
| 123. C22×C7 | #407 | semidirect |
| 136. C24 | C7×M16 | semidirect |
| 185. C7 | #20579 | direct (N × H) |
| 193. C22 | C7×#407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C4×C7 | 2 |
| C2×C7×#407 | 2 |
| C7×#1779 | 2 |
| #20579 | 7 |