Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
392 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D53 |
| commutator, socle | C23×C53 | C24 |
| Fitting | C53×#389 | C2 |
| hypercenter | #389 | D53 |
| hypocenter | C53 | #2806 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #389 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 45. C2×Dic106 | Q8 | semidirect |
| 48. C4⋊C4×C53 | Q8 | semidirect |
| 120. C53 | #2806 | semidirect |
| 165. C4⋊C4 | Dic106 | semidirect |