Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
310 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C2×D8 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C22×C8 | C23×C7 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C4×C7×C16 | C4 | semidirect |
| 10. #12889 | C7 | direct (N × H) |
| 43. C4×C16 | C4×C7 | semidirect |
| 103. C7 | #12889 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×C16 | 2 |
| C7×#1846 | 2 |
| C7×#1380 | 2 |
| #12889 | 7 |