Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 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×C4 | C22×D101 |
| commutator, socle | C22×C101 | C22×C4 |
| Fitting | #97×C101 | C2 |
| hypercenter | #97 | D101 |
| hypocenter | C101 | #435 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C2×C4 ◁ #97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13108057 | C2 | semidirect |
| 2. C2×C8×D101 | C2 | semidirect |
| 4. C4⋊#11717579 | C2 | semidirect |
| 5. #15692167 | C2 | semidirect |
| 6. #15692167 | C2 | semidirect |
| 7. #97×C101 | C2 | semidirect |
| 34. C8×C101 | D4 | semidirect |
| 43. C2×D101 | M16 | semidirect |
| 55. C101 | #435 | semidirect |
| 63. #97 | D101 | semidirect |
| 92. C8 | D404 | semidirect |