Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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×#424 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #424 | D43 |
| hypocenter | C43 | #3043 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #424 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063358 | C2 | semidirect |
| 2. C22×#10621873 | C2 | semidirect |
| 4. #14583376 | C2 | semidirect |
| 5. #14583122 | C2 | semidirect |
| 6. #14583100 | C2 | semidirect |
| 7. #14582905 | C2 | semidirect |
| 8. #14582896 | C2 | semidirect |
| 9. C43×#424 | C2 | semidirect |
| 14. C2×Dic172 | C22 | semidirect |
| 17. C2×#10621873 | C22 | semidirect |
| 22. C4×Dic86 | C22 | semidirect |
| 26. #13063250 | C22 | semidirect |
| 28. #13063247 | C22 | semidirect |
| 32. C4⋊C8×C43 | C22 | semidirect |
| 48. C2×Dic86 | D4 | semidirect |
| 123. #424 | D43 | semidirect |
| 126. C43 | #3043 | semidirect |
| 146. C4⋊C8 | C2×D43 | semidirect |