Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
192 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D53 |
| commutator | C4×C53 | C22×C8 |
| Frattini | C42 | C22×D53 |
| Fitting | C53×D4⋊C8 | C2 |
| socle | C22×C53 | C4×D4 |
| hypercenter | D4⋊C8 | D53 |
| hypocenter | C53 | #1580 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. D4×#88322 | C2 | semidirect |
| 3. #16810688 | C2 | semidirect |
| 4. #16810373 | C2 | semidirect |
| 5. #16810352 | C2 | semidirect |
| 6. #16810345 | C2 | semidirect |
| 7. C53×D4⋊C8 | C2 | semidirect |
| 32. #11719922 | C8 | semidirect |
| 45. D4×C53 | C2×C8 | semidirect |
| 54. D212 | C2×C8 | semidirect |
| 63. #88322 | C2×C8 | semidirect |
| 89. D4⋊C8 | D53 | semidirect |
| 91. C53 | #1580 | semidirect |
| 131. D4 | C8×D53 | semidirect |