Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D172 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#432 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #432 | D43 |
| hypocenter | C43 | #3217 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #432 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063322 | C2 | semidirect |
| 2. #14583433 | C2 | semidirect |
| 3. #14583288 | C2 | semidirect |
| 4. #14583264 | C2 | semidirect |
| 5. #14583100 | C2 | semidirect |
| 6. #14583095 | C2 | semidirect |
| 7. #14583052 | C2 | semidirect |
| 8. #14583035 | C2 | semidirect |
| 9. C43×#432 | C2 | semidirect |
| 13. C2×#10621873 | C22 | semidirect |
| 14. C2×D344 | C22 | semidirect |
| 20. #13063317 | C22 | semidirect |
| 21. #13063313 | C22 | semidirect |
| 25. C4×Dic86 | C22 | semidirect |
| 26. C4×D172 | C22 | semidirect |
| 29. #13063247 | C22 | semidirect |
| 30. #13063247 | C22 | semidirect |
| 32. C4⋊C8×C43 | C22 | semidirect |
| 34. #97×C43 | C22 | semidirect |
| 136. #432 | D43 | semidirect |
| 137. C43 | #3217 | semidirect |
| 158. C4⋊C8 | C2×D43 | semidirect |
| 162. #97 | C2×D43 | semidirect |