Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1492 conjugacy classes of subgroups; only the 553 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 553 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D43 |
| commutator, socle | C22×C43 | C25 |
| Fitting | C43×#519 | C2 |
| hypercenter | #519 | D43 |
| hypocenter | C43 | #3486 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063373 | C2 | semidirect |
| 2. C22×Q8×D43 | C2 | semidirect |
| 3. Q8×D172 | C2 | semidirect |
| 4. #14583561 | C2 | semidirect |
| 5. #14583475 | C2 | semidirect |
| 6. #14583411 | C2 | semidirect |
| 7. C43×#519 | C2 | semidirect |
| 9. C2×#10621902 | C22 | semidirect |
| 14. C2×Q8×D43 | C22 | semidirect |
| 16. #13063325 | C22 | semidirect |
| 17. #13063313 | C22 | semidirect |
| 20. #13063305 | C22 | semidirect |
| 25. C4×Q8×C43 | C22 | semidirect |
| 28. C2×Q8×C43 | D4 | semidirect |
| 78. C2×D43 | 2−1+4 | semidirect |
| 95. #519 | D43 | semidirect |
| 96. C43 | #3486 | semidirect |
| 113. C4×Q8 | C2×D43 | semidirect |
| 124. C2×Q8 | D172 | semidirect |