Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
650 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 122 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 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C2×C4×C7×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C7×#509 | C2 | semidirect |
| 2. C2×C7×#493 | C2 | semidirect |
| 3. C2×C7×#361 | C2 | semidirect |
| 4. C7×#1974 | C2 | semidirect |
| 5. C7×#1376 | C2 | semidirect |
| 21. #13331 | C7 | direct (N × H) |
| 27. C2×C7×Q16 | D4 | semidirect |
| 38. C2×C7×D8 | D4 | semidirect |
| 48. C7×M32 | D4 | semidirect |
| 54. C2×#509 | C2×C7 | semidirect |
| 55. C2×#493 | C2×C7 | semidirect |
| 56. C2×#361 | C2×C7 | semidirect |
| 57. #1974 | C2×C7 | semidirect |
| 58. #1376 | C2×C7 | semidirect |
| 151. C2×Q16 | C7×D4 | semidirect |
| 162. C2×D8 | C7×D4 | semidirect |
| 172. M32 | C7×D4 | semidirect |
| 272. C7 | #13331 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#509 | 2 |
| C2×C7×#493 | 2 |
| C2×C7×#361 | 2 |
| C7×#1974 | 2 |
| C7×#1376 | 2 |
| #13331 | 7 |