Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
348 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 104 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 | C2×M16×C53 | C4 |
| hypercenter | C2×M16 | #6157 |
| hypocenter | C53 | #1753 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M16 | |
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 |
| 13. #13133274 | C4 | semidirect |
| 14. C22⋊#88324 | C4 | semidirect |
| 19. C2×#11719917 | C4 | semidirect |
| 20. C2×#11719912 | C4 | semidirect |
| 21. C2×#11719912 | C4 | semidirect |
| 26. C2×M16×C53 | C4 | semidirect |
| 75. C2×#6157 | M16 | semidirect |
| 97. C8×C53 | C22⋊C4 | semidirect |
| 99. #88322 | C22⋊C4 | semidirect |
| 136. C53 | #1753 | semidirect |
| 143. C2×M16 | #6157 | semidirect |
| 228. C8 | C22⋊#6157 | semidirect |