Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
168 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C42×D71 |
| commutator | C4×C71 | C2×C42 |
| Frattini | C2×C8 | C22×D71 |
| Fitting | #347×C71 | C2 |
| socle | C2×C71 | C2×#97 |
| hypercenter | #347 | D71 |
| hypocenter | C71 | C2×#347 |
| LCS | G ▷ C4×C71 ▷ C71 | |
| UCS | C1 ◁ C4 ◁ #347 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #17985777 | C2 | semidirect |
| 4. #17985776 | C2 | semidirect |
| 5. #347×C71 | C2 | semidirect |
| 10. #14556067 | C4 | semidirect |
| 11. C16×D71 | C4 | semidirect |
| 27. C71⋊C16 | C2×C4 | semidirect |
| 31. C16×C71 | C2×C4 | semidirect |
| 59. D71 | #347 | direct (N × H) |
| 61. C71 | C2×#347 | semidirect |
| 66. #347 | D71 | direct (N × H) |
| 92. C16 | C4×D71 | semidirect |