Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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 | C23×D101 |
| commutator, socle | C22×C101 | C24 |
| Fitting | #124×C101 | C2 |
| hypercenter | #124 | D101 |
| hypocenter | C101 | #546 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13108075 | C2 | semidirect |
| 2. C2×D4×D101 | C2 | semidirect |
| 3. #15692237 | C2 | semidirect |
| 4. #15692231 | C2 | semidirect |
| 5. #15692228 | C2 | semidirect |
| 6. #15692226 | C2 | semidirect |
| 7. #15692225 | C2 | semidirect |
| 8. C4×D404 | C2 | semidirect |
| 9. C4×D404 | C2 | semidirect |
| 10. C22⋊C4×D101 | C2 | semidirect |
| 11. #124×C101 | C2 | semidirect |
| 16. C2×D404 | C22 | semidirect |
| 18. C2×C22⋊D101 | C22 | semidirect |
| 21. C2×C4×D101 | C22 | semidirect |
| 22. C2×C4×D101 | C22 | semidirect |
| 23. C2×C4×D101 | C22 | semidirect |
| 24. C4⋊Dic101 | C22 | semidirect |
| 25. C4⋊Dic101 | C22 | semidirect |
| 26. #13108053 | C22 | semidirect |
| 27. C22⋊Dic101 | C22 | semidirect |
| 30. #13108051 | C22 | semidirect |
| 31. #13108051 | C22 | semidirect |
| 32. C2×Q8×C101 | C22 | semidirect |
| 34. C22⋊C4×C101 | C22 | semidirect |
| 35. C22⋊C4×C101 | C22 | semidirect |
| 36. C42×C101 | C22 | semidirect |
| 57. D404 | D4 | semidirect |
| 75. C2×D101 | #41 | semidirect |
| 90. C101 | #546 | semidirect |
| 94. #124 | D101 | semidirect |
| 105. C2×Q8 | C2×D101 | semidirect |
| 125. C22⋊C4 | C2×D101 | semidirect |
| 126. C22⋊C4 | C2×D101 | semidirect |
| 127. C42 | C2×D101 | semidirect |