Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
164 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 71 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×C8 | C22×D53 |
| commutator, socle | C22×C53 | C22×C8 |
| Fitting | C53×C22⋊C16 | C2 |
| hypercenter | C22⋊C16 | D53 |
| hypocenter | C53 | #2168 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C8 ◁ C22⋊C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133156 | C2 | semidirect |
| 2. C22×#11719908 | C2 | semidirect |
| 4. #16810441 | C2 | semidirect |
| 5. #16810402 | C2 | semidirect |
| 6. #16810398 | C2 | semidirect |
| 7. C53×C22⋊C16 | C2 | semidirect |
| 39. #11719908 | D4 | semidirect |
| 59. C22×C53 | M32 | semidirect |
| 81. C22⋊C16 | D53 | semidirect |
| 83. C53 | #2168 | semidirect |
| 138. C22 | #13133156 | semidirect |