Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
424 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D71 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #500×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #500 | D71 |
| hypocenter | C71 | C2×#500 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #500 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17986404 | C2 | semidirect |
| 3. #17986403 | C2 | semidirect |
| 4. #17986402 | C2 | semidirect |
| 7. #500×C71 | C2 | semidirect |
| 32. C8×D71 | Q8 | semidirect |
| 61. C8×C71 | C2×Q8 | semidirect |
| 62. C71⋊C8 | C2×Q8 | semidirect |
| 78. D71 | #500 | direct (N × H) |
| 80. C71 | C2×#500 | semidirect |
| 85. #500 | D71 | direct (N × H) |
| 142. C8 | Q8×D71 | semidirect |