Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1334 conjugacy classes of subgroups; only the 366 normal subgroups are shown.
This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 366 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 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C24 | C24×C7 |
| prime radical | C2×C7×#537 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C7×C4⋊C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#2313 | C2 | semidirect |
| 3. C7×#1964 | C2 | semidirect |
| 4. C7×#1782 | C2 | semidirect |
| 7. C2×C7×C22⋊Q8 | C4 | semidirect |
| 8. C2×C7×#121 | C4 | semidirect |
| 16. #21796 | C7 | direct (N × H) |
| 42. #2313 | C2×C7 | semidirect |
| 43. #1964 | C2×C7 | semidirect |
| 44. #1782 | C2×C7 | semidirect |
| 75. C2×C22⋊Q8 | C4×C7 | semidirect |
| 76. C2×#121 | C4×C7 | semidirect |
| 210. C7 | #21796 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#537 | 2 |
| C7×#2313 | 2 |
| C7×#1964 | 2 |
| C7×#1782 | 2 |
| #21796 | 7 |