Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
174 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 90 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 | C22×#6157 |
| commutator | C2×C53 | C22×C16 |
| Fitting | C4×D4×C53 | C4 |
| socle | C22×C53 | C22×C8 |
| hypercenter | C4×D4 | #6157 |
| hypocenter | C53 | D4×C16 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11719910 | C2 | semidirect |
| 2. C4⋊#11719910 | C2 | semidirect |
| 3. C22⋊#11719910 | C2 | semidirect |
| 4. C4×#11719910 | C2 | semidirect |
| 27. #11719910 | D4 | direct (N × H) |
| 29. D4×C53 | C16 | semidirect |
| 42. C22×C53 | C2×C16 | semidirect |
| 46. C4×C53 | C2×C16 | semidirect |
| 59. C53 | D4×C16 | semidirect |
| 83. D4 | #11719910 | direct (N × H) |
| 96. C22 | C2×#11719910 | semidirect |
| 100. C4 | C2×#11719910 | semidirect |