Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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×#423 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #423 | D47 |
| hypocenter | C47 | #3038 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #423 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13094052 | C2 | semidirect |
| 2. C2×#13094021 | C2 | semidirect |
| 3. C4×#10625350 | C2 | semidirect |
| 4. #15689324 | C2 | semidirect |
| 5. #15689319 | C2 | semidirect |
| 6. #15689129 | C2 | semidirect |
| 7. C47×#423 | C2 | semidirect |
| 12. C2×#10625325 | C22 | semidirect |
| 13. C2×D376 | C22 | semidirect |
| 17. C4×Dic94 | C22 | semidirect |
| 18. C4×D188 | C22 | semidirect |
| 23. #13093946 | C22 | semidirect |
| 26. C4⋊C8×C47 | C22 | semidirect |
| 32. #10625350 | D4 | semidirect |
| 78. D188 | C2×D4 | semidirect |
| 82. Dic94 | C2×D4 | semidirect |
| 94. C4×C47 | AGL(1,ℤ/8) | semidirect |
| 110. #423 | D47 | semidirect |
| 112. C47 | #3038 | semidirect |
| 130. C4⋊C8 | C2×D47 | semidirect |
| 201. C4 | #13094052 | semidirect |