Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
632 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 632 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 | C4×C7 | B(4,𝔽2) |
| commutator | C2×D4 | C22×C4×C7 |
| Frattini, cosocle | C2×#41 | C23×C7 |
| socle | C2×C7 | #1889 |
| prime radical | C7×#3018 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C2×C4×C7 ◁ C2×C7×#41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#2979 | C2 | semidirect |
| 3. C7×#2132 | C2 | semidirect |
| 4. C7×#1791 | C2 | semidirect |
| 5. C7×#1392 | C2 | semidirect |
| 25. #13051 | C7 | direct (N × H) |
| 70. #2979 | C2×C7 | semidirect |
| 71. #2132 | C2×C7 | semidirect |
| 72. #1791 | C2×C7 | semidirect |
| 73. #1392 | C2×C7 | semidirect |
| 362. C7 | #13051 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3018 | 2 |
| C7×#2979 | 2 |
| C7×#2132 | 2 |
| C7×#1791 | 2 |
| C7×#1392 | 2 |
| #13051 | 7 |