Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
418 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 130 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 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C22×C7×D8 | C22 |
| LCS | G ▷ C22×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 |
|---|---|---|
| 1. C2×C7×#499 | C2 | semidirect |
| 4. C7×#1380 | C2 | semidirect |
| 5. C7×#1374 | C2 | semidirect |
| 17. #13365 | C7 | direct (N × H) |
| 41. C2×#499 | C2×C7 | semidirect |
| 44. #1380 | C2×C7 | semidirect |
| 45. #1374 | C2×C7 | semidirect |
| 215. C7 | #13365 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#499 | 2 |
| C2×C7×#357 | 2 |
| C7×#1970 | 2 |
| C7×#1380 | 2 |
| C7×#1374 | 2 |
| #13365 | 7 |