Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14556100 |
| commutator | C2×C4×C71 | C22×C4 |
| Frattini | C22×C4 | C22×D71 |
| Fitting | #421×C71 | C2 |
| socle | C2×C71 | #390 |
| hypercenter | #421 | D71 |
| hypocenter | C71 | #1976 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #421 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17986035 | C2 | semidirect |
| 3. #17986015 | C2 | semidirect |
| 4. #17985973 | C2 | semidirect |
| 5. #17985972 | C2 | semidirect |
| 6. #17985957 | C2 | semidirect |
| 7. #421×C71 | C2 | semidirect |
| 13. C2×#11765855 | C4 | semidirect |
| 14. C2×#11765853 | C4 | semidirect |
| 15. C2×#11765852 | C4 | semidirect |
| 16. C2×#11765850 | C4 | semidirect |
| 133. C71 | #1976 | semidirect |
| 137. #421 | D71 | semidirect |