Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D43 |
| commutator, socle | C22×C43 | C23×C4 |
| Fitting | C43×#424 | C2 |
| hypercenter | #424 | D43 |
| hypocenter | C43 | #2930 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ #424 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063333 | C2 | semidirect |
| 2. C22×#10621872 | C2 | semidirect |
| 4. #14582976 | C2 | semidirect |
| 5. #14582969 | C2 | semidirect |
| 6. #14582865 | C2 | semidirect |
| 7. #14582862 | C2 | semidirect |
| 8. #14582855 | C2 | semidirect |
| 9. C43×#424 | C2 | semidirect |
| 17. C2×#10621872 | C22 | semidirect |
| 19. C2×C8×D43 | C22 | semidirect |
| 26. (C2×D43)⋊C8 | C22 | semidirect |
| 27. #13063236 | C22 | semidirect |
| 28. C4×C43⋊C8 | C22 | semidirect |
| 32. C4⋊C8×C43 | C22 | semidirect |
| 58. C2×C43⋊C8 | D4 | semidirect |
| 119. #424 | D43 | semidirect |
| 123. C43 | #2930 | semidirect |
| 142. C4⋊C8 | C2×D43 | semidirect |