Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
152 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D53 |
| commutator | C2×C4×C53 | C22×C4 |
| Frattini | C42 | C22×D53 |
| Fitting | C53×#335 | C2 |
| socle | C22×C53 | C4×D4 |
| hypercenter | #335 | D53 |
| hypocenter | C53 | #1591 |
| LCS | G ▷ C2×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ #335 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 40. #88322 | Q16 | semidirect |
| 58. C53 | #1591 | semidirect |