Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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×#408 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #408 | D43 |
| hypocenter | C43 | #3009 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C2×#41 ◁ #408 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13063358 | C2 | semidirect |
| 3. C22×#10621873 | C2 | semidirect |
| 4. #14583470 | C2 | semidirect |
| 5. #14583063 | C2 | semidirect |
| 6. #14583052 | C2 | semidirect |
| 7. #14582905 | C2 | semidirect |
| 8. #14582896 | C2 | semidirect |
| 9. C43×#408 | C2 | semidirect |
| 15. C22×Dic86 | C22 | semidirect |
| 21. C2×Dic172 | C22 | semidirect |
| 23. C2×#10621873 | C22 | semidirect |
| 24. C2×#10621873 | C22 | semidirect |
| 28. #13063304 | C22 | semidirect |
| 29. #13063284 | C22 | semidirect |
| 30. #13063250 | C22 | semidirect |
| 31. #13063247 | C22 | semidirect |
| 32. #13063247 | C22 | semidirect |
| 34. C2×M16×C43 | C22 | semidirect |
| 35. C22×C8×C43 | C22 | semidirect |
| 36. C22⋊C8×C43 | C22 | semidirect |
| 155. #408 | D43 | semidirect |
| 156. C43 | #3009 | semidirect |
| 173. C2×M16 | C2×D43 | semidirect |
| 174. C22×C8 | C2×D43 | semidirect |
| 183. C22⋊C8 | C2×D43 | semidirect |