Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
500 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 189 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×C4 | C23×D53 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C53×#423 | C2 |
| hypercenter | #423 | D53 |
| hypocenter | C53 | #2931 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #423 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133225 | C2 | semidirect |
| 3. #16810700 | C2 | semidirect |
| 4. #16810688 | C2 | semidirect |
| 5. #16810591 | C2 | semidirect |
| 6. C2×C4×#88322 | C2 | semidirect |
| 7. C53×#423 | C2 | semidirect |
| 42. C2×#88322 | D4 | semidirect |
| 75. C4×C53 | #131 | semidirect |
| 88. #423 | D53 | semidirect |
| 91. C53 | #2931 | semidirect |
| 160. C4 | #13133225 | semidirect |