Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
5294 conjugacy classes of subgroups; only the 1134 normal subgroups are shown.
This group has 5294 conjugacy classes of subgroups — too many to draw. Only its 1134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | #120 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C22×C7×H(5,𝔽2) | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C25×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C7×#123 | C2 | semidirect |
| 3. C2×C7×#458 | C2 | direct (N × H) |
| 4. C22×C7×#99 | C2 | semidirect |
| 10. C24×C4×C7 | C22 | semidirect |
| 12. C2×C7×#123 | C22 | semidirect |
| 15. C22×C7×C22⋊C4 | C22 | semidirect |
| 16. C7×#458 | C22 | direct (N × H) |
| 17. C2×C7×#99 | C22 | semidirect |
| 18. C22×#458 | C7 | direct (N × H) |
| 40. C23×C4×C7 | C23 | semidirect |
| 42. C7×#123 | C23 | semidirect |
| 46. C2×C7×C22⋊C4 | C23 | semidirect |
| 47. C7×#99 | C23 | semidirect |
| 49. C22×#123 | C2×C7 | semidirect |
| 50. C2×#458 | C2×C7 | direct (N × H) |
| 51. C22×#99 | C2×C7 | semidirect |
| 85. C22×C4×C7 | C24 | semidirect |
| 89. C7×C22⋊C4 | C24 | semidirect |
| 95. C24×C4 | C22×C7 | semidirect |
| 97. C2×#123 | C22×C7 | semidirect |
| 100. C22×C22⋊C4 | C22×C7 | semidirect |
| 101. #458 | C22×C7 | direct (N × H) |
| 102. C2×#99 | C22×C7 | semidirect |
| 154. C23×C4 | C23×C7 | semidirect |
| 156. #123 | C23×C7 | semidirect |
| 160. C2×C22⋊C4 | C23×C7 | semidirect |
| 161. #99 | C23×C7 | semidirect |
| 172. C22×C7 | #458 | direct (N × H) |
| 212. C22×C4 | C24×C7 | semidirect |
| 216. C22⋊C4 | C24×C7 | semidirect |
| 220. C2×C7 | C2×#458 | direct (N × H) |
| 252. C7 | C22×#458 | direct (N × H) |
| 263. C22 | C7×#458 | direct (N × H) |
| 273. C2 | C2×C7×#458 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×H(5,𝔽2) | 2 |
| C22×C7×#123 | 2 |
| C2×C7×#458 | 2 |
| C22×C7×#99 | 2 |
| C22×#458 | 7 |