Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
676 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator, socle | C23×C71 | C24 |
| Fitting | #390×C71 | C2 |
| hypercenter | #390 | D71 |
| hypocenter | C71 | #2548 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14556116 | C2 | semidirect |
| 3. C2×#14556115 | C2 | semidirect |
| 4. C2×#14556093 | C2 | semidirect |
| 5. #17985914 | C2 | semidirect |
| 6. #17985900 | C2 | semidirect |
| 7. #17985899 | C2 | semidirect |
| 8. C4×Dic71⋊C4 | C2 | semidirect |
| 9. #390×C71 | C2 | semidirect |
| 34. C2×Dic142 | D4 | semidirect |
| 119. Dic71 | #124 | semidirect |
| 128. C71 | #2548 | semidirect |
| 136. #390 | D71 | semidirect |