Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
532 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C7 | C24 |
| commutator | C2 | C23×C3×C4×C7 |
| Frattini, cosocle | C22 | C24×C3×C7 |
| prime radical | C23×C3×C7 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C4×C7×Q8 | C2 | semidirect |
| 4. C7×#519 | C3 | direct (N × H) |
| 5. C2×C3×C7×Q8 | C4 | semidirect |
| 12. C4×C7×Q8 | C2×C3 | semidirect |
| 14. C3×#519 | C7 | direct (N × H) |
| 20. C2×C7×Q8 | C3×C4 | semidirect |
| 27. C3×C4×Q8 | C2×C7 | semidirect |
| 34. #519 | C3×C7 | direct (N × H) |
| 40. C2×C3×Q8 | C4×C7 | semidirect |
| 50. C4×Q8 | C2×C3×C7 | semidirect |
| 62. C3×C7 | #519 | direct (N × H) |
| 63. C2×Q8 | C3×C4×C7 | semidirect |
| 82. C7 | C3×#519 | direct (N × H) |
| 91. C3 | C7×#519 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×Q8 | 2 |
| C3×C4×C7×Q8 | 2 |
| C3×C7×#117 | 2 |
| C7×#519 | 3 |
| C3×#519 | 7 |