Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 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 | C2 | C22×D404 |
| commutator | C4×C101 | C24 |
| Frattini | C4 | C23×D101 |
| Fitting | #131×C101 | C2 |
| socle | C2×C101 | C22×D4 |
| hypercenter | #131 | D101 |
| hypocenter | C101 | #577 |
| LCS | G ▷ C4×C101 ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15692302 | C2 | semidirect |
| 2. #15692301 | C2 | semidirect |
| 3. #15692288 | C2 | semidirect |
| 4. #15692283 | C2 | semidirect |
| 5. #15692277 | C2 | semidirect |
| 6. C2×#13108063 | C2 | semidirect |
| 7. #131×C101 | C2 | semidirect |
| 10. #13108074 | C22 | semidirect |
| 12. C2×Dic202 | C22 | semidirect |
| 16. Dic404 | C22 | semidirect |
| 17. #13108063 | C22 | semidirect |
| 18. #13108063 | C22 | semidirect |
| 19. #13108063 | C22 | semidirect |
| 20. D808 | C22 | semidirect |
| 22. M16×C101 | C22 | semidirect |
| 23. C2×C8×C101 | C22 | semidirect |
| 53. C101 | #577 | semidirect |
| 61. #131 | D101 | semidirect |
| 76. M16 | C2×D101 | semidirect |
| 77. C2×C8 | C2×D101 | semidirect |