Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
362 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16810503 |
| commutator | C2×C4×C53 | C22×C4 |
| Frattini | C22×C4 | C22×D53 |
| Fitting | C53×#535 | C2 |
| socle | C2×C53 | #386 |
| hypercenter | #535 | D53 |
| hypocenter | C53 | #1911 |
| LCS | G ▷ C2×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #535 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811098 | C2 | semidirect |
| 2. #16810640 | C2 | semidirect |
| 3. C2×#13133134 | C2 | semidirect |
| 4. #16810379 | C2 | semidirect |
| 14. #127×C53 | C4 | semidirect |
| 15. #124×C53 | C4 | semidirect |
| 22. C2×Q8×C53 | C2×C4 | semidirect |
| 28. C2×D4×C53 | C2×C4 | semidirect |
| 36. C42×C53 | C2×C4 | semidirect |
| 40. C4×Dic53 | D4 | semidirect |
| 94. C53 | #1911 | semidirect |
| 98. #127 | Dic53 | semidirect |
| 99. #124 | Dic53 | semidirect |
| 111. C2×Q8 | C2×Dic53 | semidirect |
| 117. C2×D4 | C2×Dic53 | semidirect |
| 132. C42 | C2×Dic53 | semidirect |