Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
106 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D16×D47 |
| commutator | C16×C47 | C23 |
| Frattini | C16 | C22×D47 |
| Fitting | C47×SD64 | C2 |
| socle | C2×C47 | C2×D16 |
| hypercenter | SD64 | D47 |
| hypocenter | C47 | #2262 |
| LCS | G ▷ C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ SD64 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689556 | C2 | semidirect |
| 2. #15689552 | C2 | semidirect |
| 3. #15688963 | C2 | semidirect |
| 4. #15688962 | C2 | semidirect |
| 5. #15688958 | C2 | semidirect |
| 6. C32×D47 | C2 | semidirect |
| 7. C47×SD64 | C2 | semidirect |
| 57. SD64 | D47 | semidirect |
| 60. C47 | #2262 | semidirect |