Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 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 | #126×C101 | C2 |
| hypercenter | #126 | D101 |
| hypocenter | C101 | #538 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15692250 | C2 | semidirect |
| 2. #15692243 | C2 | semidirect |
| 3. #15692241 | C2 | semidirect |
| 4. #15692240 | C2 | semidirect |
| 5. #15692237 | C2 | semidirect |
| 6. #15692233 | C2 | semidirect |
| 7. #15692230 | C2 | semidirect |
| 8. #15692230 | C2 | semidirect |
| 9. #15692228 | C2 | semidirect |
| 10. #15692225 | C2 | semidirect |
| 11. #15692225 | C2 | semidirect |
| 12. C4×D404 | C2 | semidirect |
| 13. #15692217 | C2 | semidirect |
| 14. C22⋊C4×D101 | C2 | semidirect |
| 15. #126×C101 | C2 | semidirect |
| 17. C2×Dic202 | C22 | semidirect |
| 22. C2×D404 | C22 | semidirect |
| 27. C2×C4×D101 | C22 | semidirect |
| 28. C2×C4×D101 | C22 | semidirect |
| 29. C4⋊Dic101 | C22 | semidirect |
| 30. #13108053 | C22 | semidirect |
| 31. #13108053 | C22 | semidirect |
| 39. #13108051 | C22 | semidirect |
| 40. #13108051 | C22 | semidirect |
| 41. #13108051 | C22 | semidirect |
| 42. #13108051 | C22 | semidirect |
| 43. C4×Dic101 | C22 | semidirect |
| 44. C4⋊C4×C101 | C22 | semidirect |
| 45. C4⋊C4×C101 | C22 | semidirect |
| 46. C4⋊C4×C101 | C22 | semidirect |
| 50. C42×C101 | C22 | semidirect |
| 116. C101 | #538 | semidirect |
| 119. #126 | D101 | semidirect |
| 149. C4⋊C4 | C2×D101 | semidirect |
| 150. C4⋊C4 | C2×D101 | semidirect |
| 151. C4⋊C4 | C2×D101 | semidirect |
| 167. C42 | C2×D101 | semidirect |