Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
368 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C113 | C22 |
| commutator | C2 | C23×C8×C113 |
| Frattini, cosocle | C8 | C24×C113 |
| socle | C22×C113 | C22×C8 |
| prime radical | C2×#41×C113 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #504×C113 | C2 | direct (N × H) |
| 3. C2×M32×C113 | C2 | semidirect |
| 4. C22×C16×C113 | C2 | semidirect |
| 10. M32×C113 | C22 | semidirect |
| 13. C2×C16×C113 | C22 | semidirect |
| 43. C2×C113 | #504 | direct (N × H) |
| 45. C2×#504 | C113 | direct (N × H) |
| 46. C113 | C2×#504 | direct (N × H) |
| 48. #504 | C2×C113 | direct (N × H) |
| 49. C2×M32 | C2×C113 | semidirect |
| 50. C22×C16 | C2×C113 | semidirect |
| 56. M32 | C22×C113 | semidirect |
| 59. C2×C16 | C22×C113 | semidirect |
| 89. C2 | #504×C113 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#131×C113 | 2 |
| #504×C113 | 2 |
| C2×M32×C113 | 2 |
| C22×C16×C113 | 2 |
| C2×#504 | 113 |