Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
216 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #6157 |
| commutator, hypocenter | C53 | C2×C4×C16 |
| Frattini | C8 | C22×#6157 |
| Fitting | C2×C16×C53 | C4 |
| socle | C22×C53 | C4×C8 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C16×#6157 | C2 | direct (N × H) |
| 7. D53⋊C16 | C4 | semidirect |
| 9. C2×#11719910 | C4 | semidirect |
| 13. C2×#11719908 | C4 | semidirect |
| 14. C16×D53 | C4 | semidirect |
| 16. C2×C16×C53 | C4 | semidirect |
| 30. #11719910 | C2×C4 | semidirect |
| 31. C16×C53 | C2×C4 | semidirect |
| 32. #11719908 | C2×C4 | semidirect |
| 34. C2×#6157 | C16 | direct (N × H) |
| 51. #6157 | C2×C16 | direct (N × H) |
| 57. C2×C53 | C4×C16 | semidirect |
| 59. D53 | C4×C16 | semidirect |
| 65. C53 | C2×C4×C16 | semidirect |
| 75. C2×C16 | #6157 | direct (N × H) |
| 93. C16 | C2×#6157 | direct (N × H) |
| 119. C2 | C16×#6157 | direct (N × H) |