Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
348 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D53 |
| commutator | C22×C53 | C2×C42 |
| Fitting | C53×#336 | C2 |
| socle | C23×C53 | C22×C4 |
| hypercenter | #336 | D53 |
| hypocenter | C53 | #1753 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#13133127 | C2 | semidirect |
| 4. C2×C4×#88322 | C2 | semidirect |
| 6. #16810377 | C2 | semidirect |
| 7. C53×#336 | C2 | semidirect |
| 11. C2×#11719912 | C4 | semidirect |
| 16. #13133129 | C4 | semidirect |
| 60. C2×C4×C53 | M16 | semidirect |
| 80. #88322 | C22⋊C4 | semidirect |
| 111. #336 | D53 | semidirect |
| 112. C53 | #1753 | semidirect |
| 175. C2×C4 | #11719912 | semidirect |