Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
240 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 240 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 | #123×C101 | C2 |
| hypercenter | #123 | D101 |
| hypocenter | C101 | #540 |
| 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. #15692251 | C2 | semidirect |
| 2. #15692245 | C2 | semidirect |
| 3. #15692240 | C2 | semidirect |
| 4. #15692239 | C2 | semidirect |
| 5. #15692237 | C2 | semidirect |
| 6. #15692230 | C2 | semidirect |
| 7. #15692229 | C2 | semidirect |
| 8. #15692228 | C2 | semidirect |
| 9. #15692228 | C2 | semidirect |
| 10. #15692228 | C2 | semidirect |
| 11. #15692227 | C2 | semidirect |
| 12. C4×C22⋊D101 | C2 | semidirect |
| 13. #15692215 | C2 | semidirect |
| 14. #15692213 | C2 | semidirect |
| 15. #123×C101 | C2 | semidirect |
| 115. C101 | #540 | semidirect |
| 122. #123 | D101 | semidirect |