Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
528 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 242 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#6157 |
| commutator | C2×C53 | C23×C8 |
| Frattini | C22 | C23×#6157 |
| Fitting | C2×C42×C53 | C4 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C2×C42 | #6157 |
| hypocenter | C53 | C2×#431 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811642 | C2 | direct (N × H) |
| 2. C2×C4⋊#88324 | C2 | semidirect |
| 4. C2×C4×#88324 | C2 | semidirect |
| 7. C4⋊#88324 | C22 | semidirect |
| 9. C4×#88324 | C22 | semidirect |
| 28. C2×C4×D53 | C8 | semidirect |
| 62. C4×D53 | C2×C8 | semidirect |
| 80. C2×C53 | #431 | semidirect |
| 90. C53 | C2×#431 | semidirect |
| 165. C2 | #16811642 | direct (N × H) |