Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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 | #126×C101 | C2 |
| hypercenter | #126 | D101 |
| hypocenter | C101 | #563 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15692255 | C2 | semidirect |
| 2. #15692254 | C2 | semidirect |
| 3. #15692250 | C2 | semidirect |
| 4. #15692249 | C2 | semidirect |
| 5. #15692248 | C2 | semidirect |
| 6. #15692246 | C2 | semidirect |
| 7. #15692245 | C2 | semidirect |
| 11. #15692235 | C2 | semidirect |
| 12. #15692233 | C2 | semidirect |
| 13. #15692232 | C2 | semidirect |
| 14. #15692232 | C2 | semidirect |
| 15. #126×C101 | C2 | semidirect |
| 97. C101 | #563 | semidirect |
| 104. #126 | D101 | semidirect |