Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1144 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 389 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D47 |
| commutator | C22×C47 | C23×C4 |
| Frattini | C23 | C23×D47 |
| Fitting | C24×C4×C47 | C2 |
| socle | C24×C47 | C23 |
| hypercenter | C24×C4 | D47 |
| hypocenter | C47 | C2×#381 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C24 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15688986 | C2 | direct (N × H) |
| 3. C2×C47⋊#95 | C2 | semidirect |
| 8. C47⋊#95 | C22 | semidirect |
| 11. C23×C4×C47 | C4 | semidirect |
| 23. C22×C4×C47 | C2×C4 | semidirect |
| 60. C2×C47 | #381 | semidirect |
| 68. C47 | C2×#381 | semidirect |
| 72. C23×C4 | Dic47 | semidirect |
| 90. C22×C4 | C2×Dic47 | semidirect |
| 123. C2 | #15688986 | direct (N × H) |