Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1476 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1476 conjugacy classes of subgroups — too many to draw. Only its 557 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 | C24×D53 |
| commutator, socle | C22×C53 | C25 |
| Fitting | C4×#41×C53 | C2 |
| hypercenter | C4×#41 | D53 |
| hypocenter | C53 | #3499 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133264 | C2 | semidirect |
| 2. Q8×D212 | C2 | semidirect |
| 3. #16811277 | C2 | semidirect |
| 4. #16811199 | C2 | semidirect |
| 5. #16811173 | C2 | semidirect |
| 6. C2×#13133217 | C2 | semidirect |
| 7. C4×#41×C53 | C2 | semidirect |
| 28. #41×C53 | D4 | semidirect |
| 78. C4×C53 | 2−1+4 | semidirect |
| 91. C4×#41 | D53 | semidirect |
| 92. C53 | #3499 | semidirect |
| 115. #41 | D212 | semidirect |
| 164. C4 | #13133264 | semidirect |