Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
3294 conjugacy classes of subgroups; only the 974 normal subgroups are shown.
This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 974 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C26×C7 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#2842 | C2 | direct (N × H) |
| 2. C2×C7×#399 | C2 | semidirect |
| 3. C2×C7×#396 | C2 | semidirect |
| 6. C22×C7×C4⋊C4 | C22 | semidirect |
| 9. C7×#399 | C22 | semidirect |
| 10. C7×#396 | C22 | semidirect |
| 12. C2×C7×#95 | C22 | semidirect |
| 13. C2×#2842 | C7 | direct (N × H) |
| 21. C2×C7×C4⋊C4 | C23 | semidirect |
| 26. C7×#95 | C23 | semidirect |
| 27. #2842 | C2×C7 | direct (N × H) |
| 28. C2×#399 | C2×C7 | semidirect |
| 29. C2×#396 | C2×C7 | semidirect |
| 49. C22×C4⋊C4 | C22×C7 | semidirect |
| 52. #399 | C22×C7 | semidirect |
| 53. #396 | C22×C7 | semidirect |
| 55. C2×#95 | C22×C7 | semidirect |
| 80. C2×C4⋊C4 | C23×C7 | semidirect |
| 85. #95 | C23×C7 | semidirect |
| 117. C2×C7 | #2842 | direct (N × H) |
| 137. C7 | C2×#2842 | direct (N × H) |
| 152. C2 | C7×#2842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2842 | 2 |
| C2×C7×#399 | 2 |
| C2×C7×#396 | 2 |
| C2×C7×#379 | 2 |
| C2×#2842 | 7 |