Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
270 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 111 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 | C2×#41×C101 | C2 |
| hypercenter | C2×#41 | D101 |
| hypocenter | C101 | #536 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic202 | C2 | semidirect |
| 2. #15692253 | C2 | semidirect |
| 3. #15692242 | C2 | semidirect |
| 4. #15692236 | C2 | semidirect |
| 5. #15692234 | C2 | semidirect |
| 6. #15692214 | C2 | semidirect |
| 52. C101 | #536 | semidirect |