Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1088 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 181 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 | C4×C22⋊C4×C43 | C2 |
| hypercenter | C4×C22⋊C4 | D43 |
| hypocenter | C43 | #2435 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13063313 | C2 | semidirect |
| 3. C2×#13063304 | C2 | semidirect |
| 4. #14582817 | C2 | semidirect |
| 5. #14582801 | C2 | semidirect |
| 6. #14582754 | C2 | semidirect |
| 7. C4×C22⋊C4×C43 | C2 | semidirect |
| 9. C22×Dic86 | C22 | semidirect |
| 16. C2×C4⋊Dic43 | C22 | semidirect |
| 17. C2×Dic43⋊C4 | C22 | semidirect |
| 19. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 20. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 23. C2×C42×C43 | C22 | semidirect |
| 24. #95×C43 | C22 | semidirect |
| 85. C22×C43 | #124 | semidirect |
| 114. C4×C22⋊C4 | D43 | semidirect |
| 115. C43 | #2435 | semidirect |
| 131. C2×C42 | C2×D43 | semidirect |
| 132. #95 | C2×D43 | semidirect |
| 199. C22 | #13063313 | semidirect |