Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
348 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D53 |
| commutator | C22×C53 | C22×C8 |
| Fitting | C4×C22⋊C4×C53 | C2 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C4×C22⋊C4 | D53 |
| hypocenter | C53 | #1850 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4⋊#88322 | C2 | semidirect |
| 4. #16810378 | C2 | semidirect |
| 28. C22⋊C4×C53 | C8 | semidirect |
| 55. C2×C4×C53 | C2×C8 | semidirect |
| 67. C22×C53 | C4⋊C8 | semidirect |
| 91. C53 | #1850 | semidirect |
| 122. C22⋊C4 | #88322 | semidirect |
| 140. C2×C4 | C2×#88322 | semidirect |
| 153. C22 | C4⋊#88322 | semidirect |