Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
294 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 138 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 | C23×#87938 |
| commutator, socle | C2×C101 | C23×C4 |
| Fitting | #41×C101 | C4 |
| hypercenter | #41 | #87938 |
| hypocenter | C101 | #520 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#87938 | C2 | semidirect |
| 2. D4×#87938 | C2 | semidirect |
| 3. #15692334 | C2 | semidirect |
| 4. C2×C4⋊#87938 | C2 | semidirect |
| 12. #13108075 | C4 | semidirect |
| 13. #13108074 | C4 | semidirect |
| 14. #13108073 | C4 | semidirect |
| 18. #41×C101 | C4 | semidirect |
| 23. Q8×C101 | C2×C4 | semidirect |
| 24. D4×C101 | C2×C4 | semidirect |
| 25. C2×C4×C101 | C2×C4 | semidirect |
| 26. C22⋊D101 | C2×C4 | semidirect |
| 27. C2×Dic101 | C2×C4 | semidirect |
| 28. D404 | C2×C4 | semidirect |
| 29. C4×D101 | C2×C4 | semidirect |
| 30. C4×D101 | C2×C4 | semidirect |
| 33. Dic202 | C2×C4 | semidirect |
| 50. C101 | #520 | semidirect |
| 60. #41 | #87938 | semidirect |
| 72. Q8 | C2×#87938 | semidirect |
| 75. D4 | C2×#87938 | semidirect |
| 84. C2×C4 | C2×#87938 | semidirect |