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 | #123×C101 | C2 |
| hypercenter | #123 | D101 |
| hypocenter | C101 | #546 |
| 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×#13108074 | C2 | semidirect |
| 2. C2×D4×D101 | C2 | semidirect |
| 3. #15692241 | C2 | semidirect |
| 4. #15692240 | C2 | semidirect |
| 5. #15692233 | C2 | semidirect |
| 6. #15692230 | C2 | semidirect |
| 7. #15692228 | C2 | semidirect |
| 8. #15692227 | C2 | semidirect |
| 9. #15692225 | C2 | semidirect |
| 10. #15692225 | C2 | semidirect |
| 11. #15692217 | C2 | semidirect |
| 12. #15692215 | C2 | semidirect |
| 13. C2×#13108051 | C2 | semidirect |
| 14. C22⋊C4×D101 | C2 | semidirect |
| 15. #123×C101 | C2 | semidirect |
| 19. C2×Dic202 | C22 | semidirect |
| 22. C2×D404 | C22 | semidirect |
| 23. C2×D404 | C22 | semidirect |
| 26. C2×C22⋊D101 | C22 | semidirect |
| 27. C2×C22⋊D101 | C22 | semidirect |
| 29. C22×Dic101 | C22 | semidirect |
| 31. C2×C4×D101 | C22 | semidirect |
| 32. C2×C4×D101 | C22 | semidirect |
| 33. C2×C4×D101 | C22 | semidirect |
| 34. #13108053 | C22 | semidirect |
| 35. #13108053 | C22 | semidirect |
| 36. C22⋊Dic101 | C22 | semidirect |
| 40. #13108051 | C22 | semidirect |
| 41. #13108051 | C22 | semidirect |
| 42. #13108051 | C22 | semidirect |
| 43. #13108051 | C22 | semidirect |
| 44. #13108051 | C22 | semidirect |
| 45. C4×Dic101 | C22 | semidirect |
| 47. C22×C4×C101 | C22 | semidirect |
| 48. C4⋊C4×C101 | C22 | semidirect |
| 49. C4⋊C4×C101 | C22 | semidirect |
| 50. C22⋊C4×C101 | C22 | semidirect |
| 51. C22⋊C4×C101 | C22 | semidirect |
| 52. C22⋊C4×C101 | C22 | semidirect |
| 75. C22⋊D101 | D4 | semidirect |
| 110. C2×D101 | #41 | semidirect |
| 129. C101 | #546 | semidirect |
| 135. #123 | D101 | semidirect |
| 165. C22×C4 | C2×D101 | semidirect |
| 168. C4⋊C4 | C2×D101 | semidirect |
| 169. C4⋊C4 | C2×D101 | semidirect |
| 179. C22⋊C4 | C2×D101 | semidirect |
| 180. C22⋊C4 | C2×D101 | semidirect |
| 181. C22⋊C4 | C2×D101 | semidirect |