Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
186 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 64 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 | C22×#87938 |
| commutator, socle | C22×C101 | C22×C4 |
| Fitting | C2×Q8×C101 | C4 |
| hypercenter | C2×Q8 | #87938 |
| hypocenter | C101 | #391 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C2×Dic202 | C4 | semidirect |
| 10. C2×Dic202 | C4 | semidirect |
| 15. C2×Q8×C101 | C4 | semidirect |
| 21. C2×#87938 | Q8 | semidirect |
| 49. C101 | #391 | semidirect |
| 59. C2×Q8 | #87938 | semidirect |