Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D4×D101 |
| commutator | C4×C101 | C24 |
| Frattini | C4 | C23×D101 |
| Fitting | #137×C101 | C2 |
| socle | C2×C101 | C22×D4 |
| hypercenter | #137 | D101 |
| hypocenter | C101 | #578 |
| LCS | G ▷ C4×C101 ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #137 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15692303 | C2 | semidirect |
| 2. #15692302 | C2 | semidirect |
| 3. #15692288 | C2 | semidirect |
| 4. #15692287 | C2 | semidirect |
| 5. #15692284 | C2 | semidirect |
| 6. #15692276 | C2 | semidirect |
| 7. #15692275 | C2 | semidirect |
| 8. C2×#13108064 | C2 | semidirect |
| 9. Q16×D101 | C2 | semidirect |
| 10. #15692263 | C2 | semidirect |
| 11. #137×C101 | C2 | semidirect |
| 87. C101 | #578 | semidirect |
| 94. #137 | D101 | semidirect |