Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
180 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D71 |
| commutator | C4×C71 | C22×C8 |
| Frattini | C42 | C22×D71 |
| Fitting | #334×C71 | C2 |
| socle | C22×C71 | C2×C4⋊C4 |
| hypercenter | #334 | D71 |
| hypocenter | C71 | #1565 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ #334 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #17985752 | C2 | semidirect |
| 5. #17985751 | C2 | semidirect |
| 6. #17985749 | C2 | semidirect |
| 7. #334×C71 | C2 | semidirect |
| 27. #11765848 | C8 | semidirect |
| 56. C8×C71 | C2×C8 | semidirect |
| 60. C71⋊C8 | C2×C8 | semidirect |
| 78. C71 | #1565 | semidirect |
| 85. #334 | D71 | semidirect |
| 138. C8 | C8×D71 | semidirect |