Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 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 | C2 | D4×C22⋊D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#578 | C2 |
| socle | C2×C43 | D42 |
| hypercenter | #578 | D43 |
| hypocenter | C43 | #3293 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #578 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583714 | C2 | semidirect |
| 2. #14583713 | C2 | semidirect |
| 3. #14583277 | C2 | semidirect |
| 4. #14583174 | C2 | semidirect |
| 5. #14583172 | C2 | semidirect |
| 6. #14583171 | C2 | semidirect |
| 7. #14583082 | C2 | semidirect |
| 8. #14583080 | C2 | semidirect |
| 9. #14583016 | C2 | semidirect |
| 10. #14583014 | C2 | semidirect |
| 11. C43×#578 | C2 | semidirect |
| 149. #578 | D43 | semidirect |
| 158. C43 | #3293 | semidirect |