Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
346 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 346 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 | C22×D4×C101 | C2 |
| hypercenter | C22×D4 | D101 |
| hypocenter | C101 | #534 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊D101 | C2 | semidirect |
| 2. #15692238 | C2 | semidirect |
| 3. #15692236 | C2 | semidirect |
| 4. #15692227 | C2 | semidirect |
| 5. #15692224 | C2 | semidirect |
| 6. #15692223 | C2 | semidirect |
| 7. C2×C22⋊Dic101 | C2 | semidirect |
| 8. C22×D4×C101 | C2 | semidirect |
| 9. C23×D101 | C22 | semidirect |
| 12. C2×C22⋊D101 | C22 | semidirect |
| 13. C2×C22⋊D101 | C22 | semidirect |
| 14. C22×Dic101 | C22 | semidirect |
| 15. C22×Dic101 | C22 | semidirect |
| 16. #13108053 | C22 | semidirect |
| 17. C22⋊Dic101 | C22 | semidirect |
| 18. C22⋊Dic101 | C22 | semidirect |
| 19. C22⋊Dic101 | C22 | semidirect |
| 20. #13108051 | C22 | semidirect |
| 22. C24×C101 | C22 | semidirect |
| 25. C2×D4×C101 | C22 | semidirect |
| 26. C22×C4×C101 | C22 | semidirect |
| 30. C23×C101 | D4 | semidirect |
| 73. C101 | #534 | semidirect |
| 76. C22×D4 | D101 | semidirect |
| 85. C24 | C2×D101 | semidirect |
| 92. C2×D4 | C2×D101 | semidirect |
| 95. C22×C4 | C2×D101 | semidirect |
| 107. C23 | C22⋊D101 | semidirect |