Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
296 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 181 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 | C2×C53 | C2×C4×C8 |
| Fitting | C4×C4⋊C4×C53 | C2 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C4×C4⋊C4 | D53 |
| hypocenter | C53 | C8×C4⋊C4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C4⋊#88322 | C4 | semidirect |
| 11. C4×#88322 | C4 | semidirect |
| 20. C4⋊C4×C53 | C8 | semidirect |
| 50. #88322 | C4⋊C4 | direct (N × H) |
| 58. C4×C53 | C4×C8 | semidirect |
| 74. C53 | C8×C4⋊C4 | semidirect |
| 98. C4⋊C4 | #88322 | direct (N × H) |
| 127. C4 | C4×#88322 | semidirect |