Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
418 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 418 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 | C22×C7 | #381 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. C4×C7×C4⋊C4 | C4 | semidirect |
| 12. C7×#376 | C4 | semidirect |
| 13. C43×C7 | C4 | semidirect |
| 16. #8741 | C7 | direct (N × H) |
| 66. C4×C4⋊C4 | C4×C7 | semidirect |
| 68. #376 | C4×C7 | semidirect |
| 69. C43 | C4×C7 | semidirect |
| 173. C7 | #8741 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2298 | 2 |
| C7×#1822 | 2 |
| C7×#1820 | 2 |
| C7×#1284 | 2 |
| #8741 | 7 |