Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1504 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 525 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D47 |
| commutator | C4×C47 | C25 |
| Frattini | C4 | C24×D47 |
| Fitting | C22×D8×C47 | C2 |
| socle | C23×C47 | C2×D4 |
| hypercenter | C22×D8 | D47 |
| hypocenter | C47 | C22×#135 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#10625352 | C2 | semidirect |
| 2. C2×#13094043 | C2 | direct (N × H) |
| 3. C22×Dic188 | C2 | semidirect |
| 4. C22×#10625335 | C2 | semidirect |
| 5. C22×C8×D47 | C2 | semidirect |
| 6. C22×D8×C47 | C2 | semidirect |
| 8. C2×#10625352 | C22 | semidirect |
| 13. #13094043 | C22 | direct (N × H) |
| 14. C2×Dic188 | C22 | semidirect |
| 15. C2×#10625335 | C22 | semidirect |
| 17. C2×C8×D47 | C22 | semidirect |
| 19. C2×D8×C47 | C22 | semidirect |
| 31. #10625352 | C23 | semidirect |
| 36. D8×C47 | C23 | semidirect |
| 38. #10625335 | C23 | semidirect |
| 40. Dic188 | C23 | semidirect |
| 41. C8×D47 | C23 | semidirect |
| 63. C22×C47 | #135 | semidirect |
| 73. C2×C47 | C2×#135 | semidirect |
| 80. C22×D8 | D47 | semidirect |
| 82. C47 | C22×#135 | semidirect |
| 93. C2×D8 | C2×D47 | semidirect |
| 114. D8 | C22×D47 | semidirect |
| 141. C22 | #13094043 | direct (N × H) |
| 149. C2 | C2×#13094043 | direct (N × H) |