Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
234 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 70 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 | #380 |
| 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×C4⋊#87938 | C2 | semidirect |
| 3. (C2×#87938)⋊C4 | C2 | semidirect |
| 9. C22×Dic101 | C4 | semidirect |
| 11. C2×C4×D101 | C4 | semidirect |
| 12. C2×C4×D101 | C4 | semidirect |
| 15. C22×C4×C101 | C4 | semidirect |
| 38. C22×C101 | C4⋊C4 | semidirect |
| 44. C2×D101 | C4⋊C4 | semidirect |
| 51. C4×C101 | C22⋊C4 | semidirect |
| 53. Dic101 | C22⋊C4 | semidirect |
| 61. C101 | #380 | semidirect |
| 75. C22×C4 | #87938 | semidirect |
| 109. C22 | C4⋊#87938 | semidirect |
| 115. C4 | C22⋊#87938 | semidirect |