Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1134 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 165 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×#381 | C2 |
| hypercenter | #381 | D43 |
| hypocenter | C43 | #2613 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D172 | C2 | semidirect |
| 2. C2×#13063308 | C2 | semidirect |
| 3. C2×#13063295 | C2 | semidirect |
| 4. #14582817 | C2 | semidirect |
| 5. #14582809 | C2 | semidirect |
| 6. #14582754 | C2 | semidirect |
| 7. C43×#381 | C2 | semidirect |
| 12. C22×D172 | C22 | semidirect |
| 16. C2×Dic43⋊C4 | C22 | semidirect |
| 18. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 19. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 20. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 23. #95×C43 | C22 | semidirect |
| 28. C23×D43 | D4 | semidirect |
| 32. C22×C4×C43 | D4 | semidirect |
| 109. #381 | D43 | semidirect |
| 111. C43 | #2613 | semidirect |
| 127. #95 | C2×D43 | semidirect |
| 145. C22×C4 | D172 | semidirect |