Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
488 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 165 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 | C2×#117×C53 | C2 |
| hypercenter | C2×#117 | D53 |
| hypocenter | C53 | #2628 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C2×#117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133217 | C2 | semidirect |
| 2. #16810562 | C2 | semidirect |
| 4. #16810543 | C2 | semidirect |
| 6. #16810521 | C2 | semidirect |
| 7. #16810489 | C2 | semidirect |
| 32. C22×C4×C53 | Q8 | semidirect |
| 116. C53 | #2628 | semidirect |
| 143. C22×C4 | Dic106 | semidirect |