Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C53⋊#401 |
| commutator | C24×C53 | C23 |
| Frattini | C24 | C22×D53 |
| Fitting | C53×#342 | C2 |
| socle | C2×C53 | #401 |
| hypercenter | #342 | D53 |
| hypocenter | C53 | #2104 |
| LCS | G ▷ C24×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C24 ◁ #342 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 96. C53 | #2104 | semidirect |