Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1192 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1192 conjugacy classes of subgroups — too many to draw. Only its 645 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 | C25 |
| Frattini | C22 | C24×D47 |
| Fitting | C22×C4⋊C4×C47 | C2 |
| socle | C24×C47 | C23 |
| hypercenter | C22×C4⋊C4 | D47 |
| hypocenter | C47 | C22×#125 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13094015 | C2 | direct (N × H) |
| 10. #13094015 | C22 | direct (N × H) |
| 48. C22×C47 | #125 | semidirect |
| 59. C2×C47 | C2×#125 | semidirect |
| 69. C47 | C22×#125 | semidirect |
| 111. C22 | #13094015 | direct (N × H) |
| 121. C2 | C2×#13094015 | direct (N × H) |