Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D53 |
| commutator, socle | C22×C53 | C23×C4 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C2×C4×C8×C53 | C2 |
| hypercenter | C2×C4×C8 | D53 |
| hypocenter | C53 | #2931 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133223 | C2 | semidirect |
| 3. #16810702 | C2 | semidirect |
| 4. C8×D212 | C2 | semidirect |
| 5. #16810647 | C2 | semidirect |
| 6. #16810589 | C2 | semidirect |
| 7. C2×C4×C8×C53 | C2 | semidirect |
| 35. C2×C8×C53 | D4 | semidirect |
| 75. C4×C53 | #131 | semidirect |
| 90. C2×C4×C8 | D53 | semidirect |
| 91. C53 | #2931 | semidirect |
| 123. C2×C8 | D212 | semidirect |
| 160. C4 | #13133223 | semidirect |