Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
164 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22⋊D47 |
| commutator | C4×C47 | C22×C8 |
| Frattini | C42 | C22×D47 |
| Fitting | C8×Q8×C47 | C2 |
| socle | C22×C47 | C4×D4 |
| hypercenter | C8×Q8 | D47 |
| hypocenter | C47 | C8×Q16 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C8 ◁ C8×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 32. #10625337 | C8 | direct (N × H) |
| 53. C8×C47 | Q16 | semidirect |
| 79. C47 | C8×Q16 | semidirect |
| 129. C8 | #10625337 | direct (N × H) |