Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
458 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C7×#3245 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#1962 | C2 | semidirect |
| 3. C7×#1831 | C2 | semidirect |
| 4. C7×#1547 | C2 | semidirect |
| 5. C7×#1292 | C2 | semidirect |
| 19. #10519 | C7 | direct (N × H) |
| 46. #1962 | C2×C7 | semidirect |
| 47. #1831 | C2×C7 | semidirect |
| 48. #1547 | C2×C7 | semidirect |
| 49. #1292 | C2×C7 | semidirect |
| 82. C42×C7 | D8 | semidirect |
| 205. C42 | C7×D8 | semidirect |
| 247. C7 | #10519 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3245 | 2 |
| C7×#1962 | 2 |
| C7×#1831 | 2 |
| C7×#1547 | 2 |
| C7×#1292 | 2 |
| #10519 | 7 |