Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator | C22×C43 | C23×C4 |
| Fitting | C2×C4×Q8×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C2×C4×Q8 | D43 |
| hypocenter | C43 | #2326 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14582806 | C2 | semidirect |
| 5. #14582790 | C2 | semidirect |
| 6. #14582770 | C2 | semidirect |
| 7. #14582768 | C2 | semidirect |
| 8. #14582745 | C2 | semidirect |
| 9. C2×C4×Q8×C43 | C2 | semidirect |
| 12. #13063314 | C4 | semidirect |
| 33. C2×Q8×C43 | C2×C4 | semidirect |
| 53. (C2×D43)⋊C4 | C2×C4 | semidirect |
| 57. C4×Dic43 | C2×C4 | semidirect |
| 113. C2×C4×Q8 | D43 | semidirect |
| 121. C43 | #2326 | semidirect |
| 145. C2×Q8 | C4×D43 | semidirect |