Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
950 conjugacy classes of subgroups; only the 449 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 449 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 | C24×D47 |
| commutator, socle | C22×C47 | C25 |
| Fitting | C47×#564 | C2 |
| hypercenter | #564 | D47 |
| hypocenter | C47 | #3567 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ #564 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689871 | C2 | semidirect |
| 2. #15689826 | C2 | semidirect |
| 3. #15689805 | C2 | semidirect |
| 4. #15689729 | C2 | semidirect |
| 5. #15689721 | C2 | semidirect |
| 6. #15689658 | C2 | semidirect |
| 7. C47×#564 | C2 | semidirect |
| 100. #564 | D47 | semidirect |
| 107. C47 | #3567 | semidirect |