Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
458 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 217 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D4×D47 |
| commutator | C4×C47 | C23×C4 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#575 | C2 |
| socle | C2×C47 | C2×C4×D4 |
| hypercenter | #575 | D47 |
| hypocenter | C47 | #2956 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #575 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689890 | C2 | semidirect |
| 2. #15689245 | C2 | semidirect |
| 3. #15689240 | C2 | semidirect |
| 4. #15689172 | C2 | semidirect |
| 5. C2×#13093951 | C2 | semidirect |
| 6. M16×Dic47 | C2 | semidirect |
| 9. #13094031 | C22 | semidirect |
| 14. #13093960 | C22 | semidirect |
| 15. #13093951 | C22 | semidirect |
| 16. #13093951 | C22 | semidirect |
| 17. #13093934 | C22 | semidirect |
| 18. C8×Dic47 | C22 | semidirect |
| 20. #137×C47 | C4 | semidirect |
| 21. AGL(1,ℤ/8)×C47 | C4 | semidirect |
| 34. Q16×C47 | C2×C4 | semidirect |
| 35. SD16×C47 | C2×C4 | semidirect |
| 36. D8×C47 | C2×C4 | semidirect |
| 93. C47 | #2956 | semidirect |
| 95. #137 | Dic47 | semidirect |
| 96. AGL(1,ℤ/8) | Dic47 | semidirect |
| 120. Q16 | C2×Dic47 | semidirect |
| 121. SD16 | C2×Dic47 | semidirect |
| 122. D8 | C2×Dic47 | semidirect |