Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
456 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 185 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8 | C2×D284 |
| commutator | C4×C71 | C23×C4 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #405×C71 | C2 |
| socle | C2×C71 | C2×C4×D4 |
| hypercenter | #405 | D71 |
| hypocenter | C71 | #2955 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C8 ◁ C22×C8 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14556134 | C2 | semidirect |
| 3. #17986122 | C2 | semidirect |
| 4. #17986117 | C2 | semidirect |
| 5. #17986048 | C2 | semidirect |
| 6. #17986017 | C2 | semidirect |
| 7. #405×C71 | C2 | semidirect |
| 9. #14556161 | C4 | semidirect |
| 10. #14556156 | C4 | semidirect |
| 14. #14556134 | C22 | semidirect |
| 15. #14556134 | C22 | semidirect |
| 19. #14556064 | C22 | semidirect |
| 20. #14556056 | C22 | semidirect |
| 24. #97×C71 | C22 | semidirect |
| 25. C4×C8×C71 | C22 | semidirect |
| 90. C71 | #2955 | semidirect |
| 97. #405 | D71 | semidirect |
| 114. #97 | C2×D71 | semidirect |
| 115. C4×C8 | C2×D71 | semidirect |