Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1252 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 253 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator | C22×C47 | C23×C4 |
| Fitting | C47×#380 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | #380 | D47 |
| hypocenter | C47 | D4×C22⋊C4 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13093986 | C2 | semidirect |
| 3. C2×C22⋊C4×D47 | C2 | semidirect |
| 4. #15689024 | C2 | semidirect |
| 5. #15689001 | C2 | semidirect |
| 6. #15688978 | C2 | semidirect |
| 7. C4×C22⋊Dic47 | C2 | semidirect |
| 8. C47×#380 | C2 | semidirect |
| 11. C22×D188 | C4 | semidirect |
| 15. C22×C4×D47 | C22 | semidirect |
| 19. C2×(C2×D47)⋊C4 | C22 | semidirect |
| 20. C2×(C2×D47)⋊C4 | C22 | semidirect |
| 21. C2×(C2×D47)⋊C4 | C22 | semidirect |
| 23. C2×C4×Dic47 | C22 | semidirect |
| 24. C47⋊#95 | C22 | semidirect |
| 26. C2×C4⋊C4×C47 | C22 | semidirect |
| 28. #95×C47 | C22 | semidirect |
| 34. C23×D47 | C2×C4 | semidirect |
| 38. C22×C4×C47 | C2×C4 | semidirect |
| 48. C2×D188 | C2×C4 | semidirect |
| 49. C2×D188 | C2×C4 | semidirect |
| 57. C22⋊Dic47 | D4 | semidirect |
| 96. C2×Dic47 | C2×D4 | semidirect |
| 99. D188 | C22⋊C4 | semidirect |
| 105. C22×C47 | C4×D4 | semidirect |
| 121. C2×D47 | C2×C22⋊C4 | semidirect |
| 124. C4×C47 | C2×C22⋊C4 | semidirect |
| 141. #380 | D47 | semidirect |
| 144. C47 | D4×C22⋊C4 | semidirect |
| 154. C2×C4⋊C4 | C2×D47 | semidirect |
| 164. #95 | C2×D47 | semidirect |
| 186. C22×C4 | C4×D47 | semidirect |
| 252. C22 | #13093986 | semidirect |
| 262. C4 | C22⋊C4×D47 | semidirect |