Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
282 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D71 |
| commutator | C22×C4×C71 | C23 |
| Frattini | C22×C4 | C22×D71 |
| Fitting | #340×C71 | C2 |
| socle | C23×C71 | C2×D4 |
| hypercenter | #340 | D71 |
| hypocenter | C71 | #2057 |
| LCS | G ▷ C22×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 32. C2×C71⋊C8 | Q8 | semidirect |
| 46. C2×C8×C71 | Q8 | semidirect |
| 50. C4⋊C4×C71 | Q8 | semidirect |
| 104. C71 | #2057 | semidirect |
| 142. C2×C8 | Dic142 | semidirect |
| 151. C4⋊C4 | Dic142 | semidirect |