Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
596 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 165 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 | #405×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #405 | D71 |
| hypocenter | C71 | #3155 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556156 | C2 | semidirect |
| 2. C2×#14556150 | C2 | semidirect |
| 3. C22×D568 | C2 | semidirect |
| 4. #17986568 | C2 | semidirect |
| 5. #17986388 | C2 | semidirect |
| 6. #17986383 | C2 | semidirect |
| 7. #17986376 | C2 | semidirect |
| 8. #405×C71 | C2 | semidirect |
| 13. C2×Dic284 | C22 | semidirect |
| 14. C2×#11765854 | C22 | semidirect |
| 15. C2×#11765854 | C22 | semidirect |
| 19. C2×D568 | C22 | semidirect |
| 20. C2×D568 | C22 | semidirect |
| 21. #14556125 | C22 | semidirect |
| 22. #14556116 | C22 | semidirect |
| 28. #97×C71 | C22 | semidirect |
| 29. C4×C8×C71 | C22 | semidirect |
| 51. M16×C71 | D4 | semidirect |
| 52. C2×C8×C71 | D4 | semidirect |
| 102. C71 | #3155 | semidirect |
| 110. #405 | D71 | semidirect |
| 130. #97 | C2×D71 | semidirect |
| 131. C4×C8 | C2×D71 | semidirect |
| 152. M16 | D284 | semidirect |
| 153. C2×C8 | D284 | semidirect |