Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13133185 |
| commutator | C2×C4×C53 | C22×C4 |
| Frattini | C22×C4 | C22×D53 |
| Fitting | C53×#575 | C2 |
| socle | C2×C53 | #386 |
| hypercenter | #575 | D53 |
| hypocenter | C53 | #1881 |
| LCS | G ▷ C2×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #575 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811390 | C2 | semidirect |
| 2. #16810640 | C2 | semidirect |
| 3. #16810619 | C2 | semidirect |
| 4. #16810590 | C2 | semidirect |
| 5. #16810395 | C2 | semidirect |
| 6. #16810387 | C2 | semidirect |
| 22. #137×C53 | C4 | semidirect |
| 24. AGL(1,ℤ/8)×C53 | C4 | semidirect |
| 126. C53 | #1881 | semidirect |
| 130. #137 | Dic53 | semidirect |
| 132. AGL(1,ℤ/8) | Dic53 | semidirect |