Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
440 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 253 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 | C22×D53 |
| commutator | C2×C53 | C23×C8 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C2×C4⋊C8×C53 | C2 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C2×C4⋊C8 | D53 |
| hypocenter | C53 | C2×C8×Q8 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16810747 | C2 | direct (N × H) |
| 26. C2×Dic106 | C8 | semidirect |
| 37. C2×#88322 | Q8 | semidirect |
| 53. Dic106 | C2×C8 | semidirect |
| 56. #88322 | C2×Q8 | semidirect |
| 69. C2×C53 | C8×Q8 | semidirect |
| 79. C53 | C2×C8×Q8 | semidirect |
| 141. C2 | #16810747 | direct (N × H) |