Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
828 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 241 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D53 |
| commutator | C22×C53 | C2×C42 |
| Fitting | C22×C42×C53 | C2 |
| socle | C24×C53 | C23 |
| hypercenter | C22×C42 | D53 |
| hypocenter | C53 | #1437 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C24 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13133124 | C2 | semidirect |
| 3. C22×C42×C53 | C2 | semidirect |
| 8. C2×#11719921 | C4 | semidirect |
| 43. C22×D53 | C42 | semidirect |
| 48. C2×C4×C53 | C22⋊C4 | semidirect |
| 78. C22×C42 | D53 | semidirect |
| 80. C53 | #1437 | semidirect |
| 130. C2×C4 | #11719921 | semidirect |