Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
106 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×#87938 |
| commutator | C4×C101 | C22×C4 |
| Frattini | C4 | C22×#87938 |
| Fitting | SD16×C101 | C4 |
| socle | C2×C101 | C4×D4 |
| hypercenter | SD16 | #87938 |
| hypocenter | C101 | #443 |
| LCS | G ▷ C4×C101 ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ SD16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15692343 | C2 | semidirect |
| 2. #15692342 | C2 | semidirect |
| 3. #15692325 | C2 | semidirect |
| 4. #15692320 | C2 | semidirect |
| 5. #15692319 | C2 | semidirect |
| 6. C8×#87938 | C2 | semidirect |
| 18. #13108064 | C4 | semidirect |
| 19. #13108063 | C4 | semidirect |
| 20. #13108059 | C4 | semidirect |
| 22. SD16×C101 | C4 | semidirect |
| 51. C101 | #443 | semidirect |
| 64. SD16 | #87938 | semidirect |