Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
340 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D212 |
| commutator | C2×C4×C53 | C24 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C53×#405 | C2 |
| socle | C22×C53 | C22×D4 |
| hypercenter | #405 | D53 |
| hypocenter | C53 | #3164 |
| LCS | G ▷ C2×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16811032 | C2 | semidirect |
| 3. #16811028 | C2 | semidirect |
| 4. #16811025 | C2 | semidirect |
| 31. M16×C53 | Q8 | semidirect |
| 32. C2×C8×C53 | Q8 | semidirect |
| 89. C53 | #3164 | semidirect |
| 112. M16 | Dic106 | semidirect |
| 113. C2×C8 | Dic106 | semidirect |