Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D188 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#423 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #423 | D47 |
| hypocenter | C47 | #3040 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #423 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13094057 | C2 | semidirect |
| 3. C2×#13094012 | C2 | semidirect |
| 4. C4×#10625350 | C2 | semidirect |
| 5. #15689346 | C2 | semidirect |
| 6. #15689339 | C2 | semidirect |
| 7. #15689133 | C2 | semidirect |
| 8. #15689129 | C2 | semidirect |
| 9. C47×#423 | C2 | semidirect |
| 15. C2×Dic188 | C22 | semidirect |
| 17. C2×#10625325 | C22 | semidirect |
| 22. C4×Dic94 | C22 | semidirect |
| 23. C4×D188 | C22 | semidirect |
| 29. #13093949 | C22 | semidirect |
| 34. C4⋊C8×C47 | C22 | semidirect |
| 132. #423 | D47 | semidirect |
| 135. C47 | #3040 | semidirect |
| 158. C4⋊C8 | C2×D47 | semidirect |