Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
656 conjugacy classes of subgroups; only the 322 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 322 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#6157 |
| commutator | C2×C53 | C22×C42 |
| Frattini | C22 | C23×#6157 |
| Fitting | C2×C42×C53 | C4 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C2×C42 | #6157 |
| hypocenter | C53 | C2×C4×M16 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#11719936 | C2 | direct (N × H) |
| 3. C2×#13133272 | C2 | semidirect |
| 4. C2×C4×#88324 | C2 | semidirect |
| 6. C2×#11719936 | C4 | direct (N × H) |
| 9. #13133272 | C22 | semidirect |
| 10. C4×#88324 | C22 | semidirect |
| 34. C2×#88324 | C2×C4 | semidirect |
| 36. #11719936 | C2×C4 | direct (N × H) |
| 50. C2×C4×C53 | M16 | semidirect |
| 55. C2×Dic53 | M16 | semidirect |
| 65. #88324 | C22×C4 | semidirect |
| 76. C4×C53 | C2×M16 | semidirect |
| 79. Dic53 | C2×M16 | semidirect |
| 82. C2×C53 | C4×M16 | semidirect |
| 92. C53 | C2×C4×M16 | semidirect |
| 147. C2×C4 | #11719936 | direct (N × H) |
| 167. C4 | C2×#11719936 | direct (N × H) |
| 169. C2 | C4×#11719936 | direct (N × H) |