Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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 | #460×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #460 | D71 |
| hypocenter | C71 | #3362 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #460 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×Dic142 | C2 | semidirect |
| 3. #17986345 | C2 | semidirect |
| 4. #17986344 | C2 | semidirect |
| 5. #17986290 | C2 | semidirect |
| 6. #17986287 | C2 | semidirect |
| 7. #17986197 | C2 | semidirect |
| 8. #17986123 | C2 | semidirect |
| 9. SD16×Dic71 | C2 | semidirect |
| 10. C4×#11765852 | C2 | semidirect |
| 11. #460×C71 | C2 | semidirect |
| 77. Q8×C71 | #41 | semidirect |
| 99. Dic142 | SD16 | semidirect |
| 126. C71 | #3362 | semidirect |
| 134. #460 | D71 | semidirect |
| 206. Q8 | #11765864 | semidirect |