Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1360 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 365 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D53 |
| commutator | C22×C53 | C23×C4 |
| Frattini | C23 | C23×D53 |
| Fitting | C22×C4⋊C4×C53 | C2 |
| socle | C24×C53 | C23 |
| hypercenter | C22×C4⋊C4 | D53 |
| hypocenter | C53 | C2×#390 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#11719921 | C2 | semidirect |
| 3. C22×C4×Dic53 | C2 | semidirect |
| 4. #16810524 | C2 | direct (N × H) |
| 5. C22×C4⋊C4×C53 | C2 | semidirect |
| 9. C22×D212 | C4 | semidirect |
| 13. C2×#11719921 | C22 | semidirect |
| 15. C2×C4×Dic53 | C22 | semidirect |
| 19. C2×C4⋊C4×C53 | C22 | semidirect |
| 36. C22×Dic53 | D4 | semidirect |
| 41. C2×D212 | C2×C4 | semidirect |
| 64. C2×C4×C53 | C22⋊C4 | semidirect |
| 71. C2×Dic53 | C2×D4 | semidirect |
| 90. C4×C53 | C2×C22⋊C4 | semidirect |
| 93. C2×C53 | #390 | semidirect |
| 101. C22×C4⋊C4 | D53 | semidirect |
| 105. C53 | C2×#390 | semidirect |
| 115. C2×C4⋊C4 | C2×D53 | semidirect |
| 169. C2×C4 | #11719921 | semidirect |
| 191. C4 | C2×#11719921 | semidirect |
| 193. C2 | #16810524 | direct (N × H) |