Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
572 conjugacy classes of subgroups; only the 377 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 377 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D53 |
| commutator | C2×C53 | C22×C42 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C2×#131×C53 | C2 |
| socle | C22×C53 | C23×C4 |
| hypercenter | C2×#131 | D53 |
| hypocenter | C53 | C4×#131 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C8 ◁ C2×#131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16810581 | C2 | semidirect |
| 4. #16810578 | C2 | semidirect |
| 5. M16×Dic53 | C2 | semidirect |
| 6. C2×C8×Dic53 | C2 | semidirect |
| 8. #13133224 | C4 | semidirect |
| 21. #131×C53 | C4 | semidirect |
| 30. M16×C53 | C2×C4 | semidirect |
| 31. C2×C8×C53 | C2×C4 | semidirect |
| 39. #11719917 | C2×C4 | semidirect |
| 40. C2×#88322 | C2×C4 | semidirect |
| 64. Dic53 | #131 | direct (N × H) |
| 76. C53 | C4×#131 | semidirect |
| 79. #131 | Dic53 | direct (N × H) |
| 100. M16 | C2×Dic53 | semidirect |
| 104. C2×C8 | C2×Dic53 | semidirect |