Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 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 | #123×C101 | C2 |
| hypercenter | #123 | D101 |
| hypocenter | C101 | #525 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13108073 | C2 | semidirect |
| 2. C22×C4×D101 | C2 | semidirect |
| 3. #15692238 | C2 | semidirect |
| 4. #15692233 | C2 | semidirect |
| 5. #15692228 | C2 | semidirect |
| 6. #15692225 | C2 | semidirect |
| 7. #15692223 | C2 | semidirect |
| 8. #15692217 | C2 | semidirect |
| 9. #15692215 | C2 | semidirect |
| 10. #15692211 | C2 | semidirect |
| 11. #123×C101 | C2 | semidirect |
| 14. C2×Dic202 | C22 | semidirect |
| 18. C2×C22⋊D101 | C22 | semidirect |
| 20. C22×Dic101 | C22 | semidirect |
| 24. C2×C4×D101 | C22 | semidirect |
| 25. #13108053 | C22 | semidirect |
| 26. #13108053 | C22 | semidirect |
| 30. #13108051 | C22 | semidirect |
| 31. C4×Dic101 | C22 | semidirect |
| 34. C4⋊C4×C101 | C22 | semidirect |
| 36. C22⋊C4×C101 | C22 | semidirect |
| 52. C2×Dic101 | D4 | semidirect |
| 72. C2×D101 | #41 | semidirect |
| 86. C101 | #525 | semidirect |
| 91. #123 | D101 | semidirect |
| 116. C4⋊C4 | C2×D101 | semidirect |
| 122. C22⋊C4 | C2×D101 | semidirect |