Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D284 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #408×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #408 | D71 |
| hypocenter | C71 | #3099 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C2×#41 ◁ #408 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17986482 | C2 | semidirect |
| 3. #17986341 | C2 | semidirect |
| 4. #17986330 | C2 | semidirect |
| 5. #17986324 | C2 | semidirect |
| 6. #17986318 | C2 | semidirect |
| 7. #17986041 | C2 | semidirect |
| 8. C2×#14556060 | C2 | semidirect |
| 9. #17986001 | C2 | semidirect |
| 10. #17985996 | C2 | semidirect |
| 11. #408×C71 | C2 | semidirect |
| 134. C71 | #3099 | semidirect |
| 145. #408 | D71 | semidirect |