Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
852 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D71 |
| commutator | C22×C71 | C22×C8 |
| Fitting | C24×C4×C71 | C2 |
| socle | C23×C71 | C22×C4 |
| hypercenter | C24×C4 | D71 |
| hypocenter | C71 | #1779 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C22⋊(C71⋊C8) | C2 | semidirect |
| 3. C22×C71⋊C8 | C22 | semidirect |
| 12. C24×C71 | C8 | semidirect |
| 41. C22×C71 | C22⋊C8 | semidirect |
| 52. C71 | #1779 | semidirect |
| 63. C24 | C71⋊C8 | semidirect |
| 93. C22 | C22⋊(C71⋊C8) | semidirect |