Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
312 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 312 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, Frattini | C22 | C23×D101 |
| commutator, socle | C22×C101 | C24 |
| Fitting | #127×C101 | C2 |
| hypercenter | #127 | D101 |
| hypocenter | C101 | #550 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13108073 | C2 | semidirect |
| 2. #15692251 | C2 | semidirect |
| 3. #15692227 | C2 | semidirect |
| 4. #15692226 | C2 | semidirect |
| 5. C4×Dic202 | C2 | semidirect |
| 6. C4×D404 | C2 | semidirect |
| 7. D4×Dic101 | C2 | semidirect |
| 8. #127×C101 | C2 | semidirect |
| 42. Dic202 | D4 | semidirect |
| 52. C4×C101 | #41 | semidirect |
| 61. C101 | #550 | semidirect |
| 65. #127 | D101 | semidirect |
| 117. C4 | #13108073 | semidirect |