Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
124 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 48 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 | C22⋊C4×C101 | C4 |
| hypercenter | C22⋊C4 | #87938 |
| hypocenter | C101 | #435 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13108084 | C2 | semidirect |
| 2. C22×#11717581 | C2 | semidirect |
| 3. C4⋊#11717581 | C2 | semidirect |
| 4. #15692312 | C2 | semidirect |
| 5. C22⋊#11717581 | C2 | semidirect |
| 6. #15692310 | C2 | semidirect |
| 36. #11717581 | D4 | semidirect |
| 39. C22×C101 | M16 | semidirect |
| 55. C101 | #435 | semidirect |
| 98. C22 | #13108084 | semidirect |