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 | C22×C42×C53 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | C22×C42 | D53 |
| hypocenter | C53 | C42×D4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C42 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C42×D53 | C2 | semidirect |
| 3. C4×#11719919 | C2 | semidirect |
| 4. C4×#11719921 | C2 | semidirect |
| 5. C4×C22⋊Dic53 | C2 | semidirect |
| 6. C42×Dic53 | C2 | semidirect |
| 7. C22×C42×C53 | C2 | semidirect |
| 10. C4×C22⋊D53 | C4 | direct (N × H) |
| 27. C22×C4×C53 | C2×C4 | semidirect |
| 36. C2×C4×D53 | C2×C4 | semidirect |
| 38. C42×C53 | D4 | semidirect |
| 39. C22⋊Dic53 | C2×C4 | semidirect |
| 40. #11719921 | C2×C4 | semidirect |
| 41. #11719919 | C2×C4 | semidirect |
| 44. C4×Dic53 | C2×C4 | semidirect |
| 59. C22⋊D53 | C42 | direct (N × H) |
| 69. C22×C53 | C2×C42 | semidirect |
| 75. C2×D53 | C2×C42 | semidirect |
| 77. C4×C53 | C4×D4 | semidirect |
| 80. Dic53 | C2×C42 | semidirect |
| 89. C22×C42 | D53 | semidirect |
| 94. C53 | C42×D4 | semidirect |
| 121. C22×C4 | C4×D53 | semidirect |
| 131. C42 | C22⋊D53 | direct (N × H) |
| 159. C22 | C42×D53 | semidirect |
| 167. C4 | C4×C22⋊D53 | direct (N × H) |