Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 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×#407 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #407 | D47 |
| hypocenter | C47 | #3003 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #407 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D188 | C2 | semidirect |
| 2. C2×#13094052 | C2 | semidirect |
| 3. #15689634 | C2 | semidirect |
| 4. #15689276 | C2 | semidirect |
| 5. #15689259 | C2 | semidirect |
| 6. #15689129 | C2 | semidirect |
| 7. C47×#407 | C2 | semidirect |
| 9. C2×#10625350 | C22 | semidirect |
| 16. C2×#10625325 | C22 | semidirect |
| 17. C2×D376 | C22 | semidirect |
| 19. #13094003 | C22 | semidirect |
| 20. #13093998 | C22 | semidirect |
| 23. #13093983 | C22 | semidirect |
| 24. #13093946 | C22 | semidirect |
| 26. C2×M16×C47 | C22 | semidirect |
| 27. C22⋊C8×C47 | C22 | semidirect |
| 47. C2×D188 | D4 | semidirect |
| 49. C2×D188 | C23 | semidirect |
| 51. C2×Dic94 | C23 | semidirect |
| 53. C2×C8×C47 | C23 | semidirect |
| 57. C4⋊Dic47 | C23 | semidirect |
| 98. C22×C47 | AGL(1,ℤ/8) | semidirect |
| 124. #407 | D47 | semidirect |
| 125. C47 | #3003 | semidirect |
| 137. C2×M16 | C2×D47 | semidirect |
| 145. C22⋊C8 | C2×D47 | semidirect |
| 173. C2×C8 | C22×D47 | semidirect |
| 222. C22 | #13094052 | semidirect |