Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
394 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 394 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 | C2×C4 | C23×D71 |
| commutator, socle | C22×C71 | C23×C4 |
| Fitting | #432×C71 | C2 |
| hypercenter | #432 | D71 |
| hypocenter | C71 | #2980 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ #432 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17986072 | C2 | semidirect |
| 3. #17986069 | C2 | semidirect |
| 4. #17986056 | C2 | semidirect |
| 5. #17985964 | C2 | semidirect |
| 6. #432×C71 | C2 | semidirect |
| 89. C71 | #2980 | semidirect |
| 94. #432 | D71 | semidirect |