Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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⋊Q8×C101 | C2 |
| hypercenter | C22⋊Q8 | D101 |
| hypocenter | C101 | #525 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13108075 | C2 | semidirect |
| 2. C22×C4×D101 | C2 | semidirect |
| 3. #15692240 | C2 | semidirect |
| 4. #15692231 | C2 | semidirect |
| 5. #15692230 | C2 | semidirect |
| 6. #15692229 | C2 | semidirect |
| 7. #15692225 | C2 | semidirect |
| 8. #15692217 | C2 | semidirect |
| 9. #15692215 | C2 | semidirect |
| 10. #15692213 | C2 | semidirect |
| 11. C22⋊Q8×C101 | C2 | semidirect |
| 16. C2×D404 | C22 | semidirect |
| 24. C2×C4×D101 | C22 | semidirect |
| 25. C4⋊Dic101 | C22 | semidirect |
| 26. #13108053 | C22 | semidirect |
| 29. #13108051 | C22 | semidirect |
| 30. #13108051 | C22 | semidirect |
| 31. C4×Dic101 | C22 | semidirect |
| 32. C2×Q8×C101 | C22 | semidirect |
| 34. C4⋊C4×C101 | C22 | semidirect |
| 35. C4⋊C4×C101 | C22 | semidirect |
| 62. C4×D101 | D4 | semidirect |
| 65. C22×C101 | #41 | semidirect |
| 76. C2×D101 | #41 | semidirect |
| 91. C101 | #525 | semidirect |
| 97. C22⋊Q8 | D101 | semidirect |
| 106. C2×Q8 | C2×D101 | semidirect |
| 121. C4⋊C4 | C2×D101 | semidirect |
| 122. C4⋊C4 | C2×D101 | semidirect |
| 167. C22 | #13108075 | semidirect |