Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
348 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6157 |
| commutator, socle | C22×C53 | C2×C42 |
| Fitting | C22⋊C8×C53 | C4 |
| hypercenter | C22⋊C8 | #6157 |
| hypocenter | C53 | #1753 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C22⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13133271 | C2 | semidirect |
| 3. C2×C8×#6157 | C2 | semidirect |
| 5. (C2×#6157)⋊C8 | C2 | semidirect |
| 6. (C2×#6157)⋊C8 | C2 | semidirect |
| 8. C2×#11719936 | C4 | semidirect |
| 11. C2×#11719940 | C4 | semidirect |
| 23. C22⋊#88322 | C4 | semidirect |
| 24. #13133129 | C4 | semidirect |
| 25. #13133129 | C4 | semidirect |
| 26. C22⋊C8×C53 | C4 | semidirect |
| 73. C2×#6157 | M16 | semidirect |
| 93. #88324 | C22⋊C4 | semidirect |
| 134. C53 | #1753 | semidirect |
| 150. C22⋊C8 | #6157 | semidirect |