Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1728 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1728 conjugacy classes of subgroups — too many to draw. Only its 557 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D43 |
| commutator | C22×C43 | C25 |
| Frattini | C22 | C24×D43 |
| Fitting | C2×#127×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C2×#127 | D43 |
| hypocenter | C43 | C2×#532 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#10621900 | C2 | semidirect |
| 2. #14583447 | C2 | direct (N × H) |
| 3. C2×#13063325 | C2 | semidirect |
| 4. C2×#13063312 | C2 | semidirect |
| 5. C2×#13063296 | C2 | semidirect |
| 6. C2×D4×Dic43 | C2 | semidirect |
| 7. C2×C42×D43 | C2 | semidirect |
| 8. C2×#127×C43 | C2 | semidirect |
| 10. C2×#10621900 | C22 | semidirect |
| 16. #13063325 | C22 | semidirect |
| 17. #13063312 | C22 | semidirect |
| 18. #13063296 | C22 | semidirect |
| 19. D4×Dic43 | C22 | semidirect |
| 24. C42×D43 | C22 | semidirect |
| 27. #127×C43 | C22 | semidirect |
| 46. C2×C4×D43 | D4 | semidirect |
| 66. C2×C4×C43 | #41 | semidirect |
| 78. C4×D43 | C2×D4 | semidirect |
| 90. C4×C43 | C2×#41 | semidirect |
| 96. C2×C43 | #532 | semidirect |
| 103. C2×#127 | D43 | semidirect |
| 108. C43 | C2×#532 | semidirect |
| 119. #127 | C2×D43 | semidirect |
| 177. C2×C4 | #10621900 | semidirect |
| 193. C4 | C2×#10621900 | semidirect |
| 196. C2 | #14583447 | direct (N × H) |