Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1492 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 754 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×#6157 |
| commutator, socle | C2×C53 | C24×C4 |
| Fitting | 2−1+4×C53 | C4 |
| hypercenter | 2−1+4 | #6157 |
| hypocenter | C53 | C4×2−1+4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811692 | C2 | semidirect |
| 2. #16811691 | C2 | semidirect |
| 3. #41×#6157 | C2 | semidirect |
| 4. C2×Q8×#6157 | C2 | semidirect |
| 14. #13133265 | C4 | semidirect |
| 15. #13133264 | C4 | semidirect |
| 18. 2−1+4×C53 | C4 | semidirect |
| 21. #41×C53 | C2×C4 | semidirect |
| 22. C2×Q8×C53 | C2×C4 | semidirect |
| 23. #11719949 | C2×C4 | semidirect |
| 24. Q8×D53 | C2×C4 | semidirect |
| 26. #11719947 | C2×C4 | semidirect |
| 28. #11719945 | C2×C4 | semidirect |
| 30. C2×Dic106 | C2×C4 | semidirect |
| 58. #6157 | 2−1+4 | direct (N × H) |
| 72. C53 | C4×2−1+4 | semidirect |
| 75. 2−1+4 | #6157 | direct (N × H) |
| 89. #41 | C2×#6157 | semidirect |
| 93. C2×Q8 | C2×#6157 | semidirect |