Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
696 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C22×C42×C71 | C2 |
| hypercenter | C22×C42 | D71 |
| hypocenter | C71 | #2850 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556116 | C2 | semidirect |
| 2. C2×#14556107 | C2 | semidirect |
| 4. #17985905 | C2 | semidirect |
| 5. #17985901 | C2 | semidirect |
| 6. #17985890 | C2 | semidirect |
| 7. #17985878 | C2 | semidirect |
| 8. #17985865 | C2 | semidirect |
| 9. C22×C42×C71 | C2 | semidirect |
| 63. C42×C71 | D4 | semidirect |
| 103. C22×C71 | #124 | semidirect |
| 129. C71 | #2850 | semidirect |
| 133. C22×C42 | D71 | semidirect |
| 192. C42 | C22⋊D71 | semidirect |
| 237. C22 | #14556116 | semidirect |