Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 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 | #554 |
| 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. #15692253 | C2 | semidirect |
| 2. #15692245 | C2 | semidirect |
| 3. #15692245 | C2 | semidirect |
| 4. #15692233 | C2 | semidirect |
| 5. #15692233 | C2 | semidirect |
| 6. #15692232 | C2 | semidirect |
| 7. #15692232 | C2 | semidirect |
| 8. #15692231 | C2 | semidirect |
| 9. #15692220 | C2 | semidirect |
| 13. C2×#13108053 | C2 | semidirect |
| 14. C4⋊C4×D101 | C2 | semidirect |
| 15. C22⋊Q8×C101 | C2 | semidirect |
| 61. C22⋊D101 | Q8 | semidirect |
| 101. C101 | #554 | semidirect |
| 111. C22⋊Q8 | D101 | semidirect |