Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
124 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D101 |
| commutator, socle | C22×C101 | C22×C4 |
| Fitting | C4×D4×C101 | C2 |
| hypercenter | C4×D4 | D101 |
| hypocenter | C101 | #435 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13108058 | C2 | semidirect |
| 2. C22×#11717579 | C2 | semidirect |
| 3. C4⋊#11717579 | C2 | semidirect |
| 4. C22⋊#11717579 | C2 | semidirect |
| 5. C22⋊#11717579 | C2 | semidirect |
| 6. #15692166 | C2 | semidirect |
| 36. #11717579 | D4 | semidirect |
| 42. C22×C101 | M16 | semidirect |
| 55. C101 | #435 | semidirect |
| 98. C22 | #13108058 | semidirect |