Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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 | C4×C71 | C23×C4 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #427×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #427 | D71 |
| hypocenter | C71 | #2948 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #427 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17986473 | C2 | semidirect |
| 3. #17986110 | C2 | semidirect |
| 4. #17986081 | C2 | semidirect |
| 5. #17986003 | C2 | semidirect |
| 6. #17985954 | C2 | semidirect |
| 7. #427×C71 | C2 | semidirect |
| 9. C2×D568 | C4 | semidirect |
| 14. #14556090 | C22 | semidirect |
| 17. #14556048 | C22 | semidirect |
| 18. #14556038 | C22 | semidirect |
| 19. C8×Dic71 | C22 | semidirect |
| 22. #107×C71 | C22 | semidirect |
| 23. #106×C71 | C22 | semidirect |
| 27. C2×D284 | C2×C4 | semidirect |
| 30. D568 | C2×C4 | semidirect |
| 31. D568 | C2×C4 | semidirect |
| 39. C2×C8×C71 | C2×C4 | semidirect |
| 78. C71 | #2948 | semidirect |
| 83. #427 | D71 | semidirect |
| 97. #107 | C2×D71 | semidirect |
| 98. #106 | C2×D71 | semidirect |
| 113. C2×C8 | C4×D71 | semidirect |