Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
196 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 77 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 | C4×C53 | C22×C8 |
| Frattini | C42 | C22×D53 |
| Fitting | C8×D4×C53 | C2 |
| socle | C22×C53 | C4×D4 |
| hypercenter | C8×D4 | D53 |
| hypocenter | C53 | C8×D8 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C8 ◁ C8×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C8×D212 | C2 | semidirect |
| 3. #16810375 | C2 | semidirect |
| 4. D4⋊#88322 | C2 | semidirect |
| 5. #16810350 | C2 | semidirect |
| 6. C8×#88322 | C2 | semidirect |
| 7. C8×D4×C53 | C2 | semidirect |
| 34. #11719922 | C8 | direct (N × H) |
| 45. D4×C53 | C2×C8 | semidirect |
| 54. D212 | C2×C8 | semidirect |
| 59. C8×C53 | D8 | semidirect |
| 63. #88322 | C2×C8 | semidirect |
| 86. C8×D4 | D53 | semidirect |
| 91. C53 | C8×D8 | semidirect |
| 131. D4 | C8×D53 | semidirect |
| 147. C8 | #11719922 | direct (N × H) |