Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
386 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| socle | C2×C7 | #2054 |
| prime radical | C7×#3414 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C22×C4×C7 ◁ C7×#405 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#2151 | C2 | semidirect |
| 3. C7×#2138 | C2 | semidirect |
| 4. C7×#1976 | C2 | semidirect |
| 5. C7×#1384 | C2 | semidirect |
| 19. #13447 | C7 | direct (N × H) |
| 46. #2151 | C2×C7 | semidirect |
| 47. #2138 | C2×C7 | semidirect |
| 48. #1976 | C2×C7 | semidirect |
| 49. #1384 | C2×C7 | semidirect |
| 203. C7 | #13447 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3414 | 2 |
| C7×#2151 | 2 |
| C7×#2138 | 2 |
| C7×#1976 | 2 |
| C7×#1384 | 2 |
| #13447 | 7 |