Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
924 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 381 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | C2×D53 |
| commutator | C2×C53 | C22×C42 |
| Frattini | C23 | C23×D53 |
| Fitting | C43×C53 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | C43 | D53 |
| hypocenter | C53 | C42×D4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C42 ◁ C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C42×D53 | C2 | semidirect |
| 3. C4×C4⋊Dic53 | C2 | semidirect |
| 4. C4×#11719921 | C2 | semidirect |
| 5. C43×C53 | C2 | semidirect |
| 8. C4×D212 | C4 | direct (N × H) |
| 25. C2×C4×D53 | C2×C4 | semidirect |
| 27. C42×C53 | C2×C4 | semidirect |
| 28. C42×C53 | D4 | semidirect |
| 29. #11719921 | C2×C4 | semidirect |
| 30. C4⋊Dic53 | C2×C4 | semidirect |
| 45. D212 | C42 | direct (N × H) |
| 52. C2×D53 | C2×C42 | semidirect |
| 54. C4×C53 | C2×C42 | semidirect |
| 55. C4×C53 | C4×D4 | semidirect |
| 66. C43 | D53 | semidirect |
| 67. C53 | C42×D4 | semidirect |
| 92. C42 | C4×D53 | semidirect |
| 93. C42 | D212 | direct (N × H) |
| 117. C4 | C42×D53 | semidirect |
| 118. C4 | C4×D212 | direct (N × H) |