Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C4×C47 | C23×C4 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#405 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #405 | D47 |
| hypocenter | C47 | #2948 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15689597 | C2 | semidirect |
| 3. #15689236 | C2 | semidirect |
| 4. C4×D376 | C2 | semidirect |
| 5. #15689161 | C2 | semidirect |
| 6. #15689129 | C2 | semidirect |
| 7. C47×#405 | C2 | semidirect |
| 9. C2×D376 | C4 | semidirect |
| 12. C4×D188 | C22 | semidirect |
| 16. #13093958 | C22 | semidirect |
| 17. #13093956 | C22 | semidirect |
| 18. #13093946 | C22 | semidirect |
| 22. #97×C47 | C22 | semidirect |
| 23. C4×C8×C47 | C22 | semidirect |
| 28. C2×D188 | C2×C4 | semidirect |
| 32. C2×C8×C47 | C2×C4 | semidirect |
| 43. D376 | C2×C4 | semidirect |
| 44. D376 | C2×C4 | semidirect |
| 84. #405 | D47 | semidirect |
| 85. C47 | #2948 | semidirect |
| 100. #97 | C2×D47 | semidirect |
| 101. C4×C8 | C2×D47 | semidirect |
| 112. C2×C8 | C4×D47 | semidirect |