Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2222 conjugacy classes of subgroups.
The subgroup lattice has 224 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C7 | C23 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C2×C4 | C25×C7 |
| socle, prime radical | C24×C7 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C7×#446 | C2 | direct (N × H) |
| 17. C7×#446 | C22 | direct (N × H) |
| 22. C22×#446 | C7 | direct (N × H) |
| 32. C22×C7×C8 | Q8 | semidirect |
| 49. C2×#446 | C2×C7 | direct (N × H) |
| 71. C2×C7×C8 | C2×Q8 | semidirect |
| 91. #446 | C22×C7 | direct (N × H) |
| 116. C7×C8 | C22×Q8 | semidirect |
| 126. C22×C8 | C7×Q8 | semidirect |
| 142. C22×C7 | #446 | direct (N × H) |
| 171. C2×C8 | C2×C7×Q8 | semidirect |
| 181. C2×C7 | C2×#446 | direct (N × H) |
| 205. C8 | C22×C7×Q8 | semidirect |
| 206. C7 | C22×#446 | direct (N × H) |
| 207. C22 | C7×#446 | direct (N × H) |
| 219. C2 | C2×C7×#446 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C7×Q8 | 2 |
| C2×C7×#446 | 2 |
| C22×C7×C4⋊C8 | 2 |
| C22×C7×#97 | 2 |
| C22×C4×C7×C8 | 2 |
| C22×#446 | 7 |