Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
488 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D71 |
| commutator | C22×C71 | C23×C4 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | C2×C4⋊C8×C71 | C2 |
| socle | C23×C71 | C22×C4 |
| hypercenter | C2×C4⋊C8 | D71 |
| hypocenter | C71 | C2×#432 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17986055 | C2 | direct (N × H) |
| 3. C2×C4⋊(C71⋊C8) | C2 | semidirect |
| 5. C2×#14556038 | C2 | semidirect |
| 6. C2×C4⋊C8×C71 | C2 | semidirect |
| 16. C4⋊(C71⋊C8) | C22 | semidirect |
| 18. #14556038 | C22 | semidirect |
| 21. C4⋊C8×C71 | C22 | semidirect |
| 89. C2×C71 | #432 | semidirect |
| 95. C71 | C2×#432 | semidirect |
| 99. C2×C4⋊C8 | D71 | semidirect |
| 114. C4⋊C8 | C2×D71 | semidirect |
| 185. C2 | #17986055 | direct (N × H) |