Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 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×D71 |
| commutator | C16×C71 | C23 |
| Frattini | C16 | C22×D71 |
| Fitting | Q64×C71 | C2 |
| socle | C2×C71 | C2×D16 |
| hypercenter | Q64 | D71 |
| hypocenter | C71 | #2264 |
| LCS | G ▷ C16×C71 ▷ C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q64 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q32×D71 | C2 | semidirect |
| 3. #17985839 | C2 | semidirect |
| 4. #17985838 | C2 | semidirect |
| 5. #17985836 | C2 | semidirect |
| 6. #17985832 | C2 | semidirect |
| 7. Q64×C71 | C2 | semidirect |
| 52. C71 | #2264 | semidirect |
| 56. Q64 | D71 | semidirect |