Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1088 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C43×#390 | C2 |
| hypercenter | #390 | D43 |
| hypocenter | C43 | #2435 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13063313 | C2 | semidirect |
| 3. C2×#13063312 | C2 | semidirect |
| 4. C2×#13063305 | C2 | semidirect |
| 5. #14582815 | C2 | semidirect |
| 6. #14582800 | C2 | semidirect |
| 7. #14582754 | C2 | semidirect |
| 8. C4×(C2×D43)⋊C4 | C2 | semidirect |
| 9. C43×#390 | C2 | semidirect |
| 11. C22×Dic86 | C22 | semidirect |
| 21. C2×C4⋊Dic43 | C22 | semidirect |
| 22. C2×C22⋊Dic43 | C22 | semidirect |
| 25. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 26. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 27. C2×C4×Dic43 | C22 | semidirect |
| 28. C43⋊#95 | C22 | semidirect |
| 30. C2×C4⋊C4×C43 | C22 | semidirect |
| 31. C2×C22⋊C4×C43 | C22 | semidirect |
| 32. C2×C42×C43 | C22 | semidirect |
| 136. C2×D43 | #124 | semidirect |
| 158. #390 | D43 | semidirect |
| 161. C43 | #2435 | semidirect |
| 175. C2×C4⋊C4 | C2×D43 | semidirect |
| 181. C2×C22⋊C4 | C2×D43 | semidirect |
| 183. C2×C42 | C2×D43 | semidirect |