Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
156 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C71⋊#95 |
| commutator | C2×C4×C71 | C42 |
| Frattini | C2×C42 | C2×D71 |
| Fitting | #382×C71 | C2 |
| socle | C22×C71 | #95 |
| hypercenter | #382 | D71 |
| hypocenter | C71 | #1286 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C4⋊(C71⋊C8) | C4 | semidirect |
| 9. C4×C71⋊C8 | C4 | semidirect |
| 66. C71 | #1286 | semidirect |