Finite Group DatabasebetaFinite Group DatabasebetaOrder 6464.
310 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 310 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 | #127×C101 | C2 |
| hypercenter | #127 | D101 |
| hypocenter | C101 | #532 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13108073 | C2 | semidirect |
| 2. #15692255 | C2 | semidirect |
| 3. #15692242 | C2 | semidirect |
| 4. #15692226 | C2 | semidirect |
| 5. D4×Dic101 | C2 | semidirect |
| 6. C42×D101 | C2 | semidirect |
| 7. #127×C101 | C2 | semidirect |
| 33. C4×D101 | D4 | semidirect |
| 41. C4×C101 | #41 | semidirect |
| 49. C101 | #532 | semidirect |
| 53. #127 | D101 | semidirect |
| 94. C4 | #13108073 | semidirect |