Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
712 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 154 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 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C7×#2537 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C7×#476 | C2 | semidirect |
| 3. C7×#1956 | C2 | semidirect |
| 4. C2×C7×D4⋊C8 | C2 | semidirect |
| 5. C7×#1296 | C2 | semidirect |
| 20. #10235 | C7 | direct (N × H) |
| 29. C7×C4⋊Q8 | D4 | semidirect |
| 45. C7×C4⋊C8 | D4 | semidirect |
| 50. C2×#476 | C2×C7 | semidirect |
| 52. #1956 | C2×C7 | semidirect |
| 53. C2×D4⋊C8 | C2×C7 | semidirect |
| 54. #1296 | C2×C7 | semidirect |
| 159. C4⋊Q8 | C7×D4 | semidirect |
| 175. C4⋊C8 | C7×D4 | semidirect |
| 289. C7 | #10235 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#476 | 2 |
| C7×#2537 | 2 |
| C7×#1956 | 2 |
| C2×C7×D4⋊C8 | 2 |
| C7×#1296 | 2 |
| #10235 | 7 |