Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1536 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1536 conjugacy classes of subgroups — too many to draw. Only its 549 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 | C22×#41×C43 | C2 |
| hypercenter | C22×#41 | D43 |
| hypocenter | C43 | #3487 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063373 | C2 | semidirect |
| 2. #14583568 | C2 | semidirect |
| 3. #14583556 | C2 | semidirect |
| 4. #14583466 | C2 | semidirect |
| 5. #14583410 | C2 | semidirect |
| 6. #14583377 | C2 | semidirect |
| 7. C22×#41×C43 | C2 | semidirect |
| 9. C2×#10621902 | C22 | semidirect |
| 11. C2×Q8×D43 | C22 | semidirect |
| 12. #13063321 | C22 | semidirect |
| 13. #13063312 | C22 | semidirect |
| 15. #13063304 | C22 | semidirect |
| 16. #13063299 | C22 | semidirect |
| 17. #13063296 | C22 | semidirect |
| 19. Q8×Dic43 | C22 | semidirect |
| 20. C4×C22⋊D43 | C22 | semidirect |
| 29. C2×Q8×C43 | D4 | semidirect |
| 89. C22×#41 | D43 | semidirect |
| 95. C43 | #3487 | semidirect |
| 121. C2×Q8 | C22⋊D43 | semidirect |