Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 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×#407 | C2 |
| hypercenter | #407 | D43 |
| hypocenter | C43 | #2920 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ #407 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14582953 | C2 | semidirect |
| 3. #14582949 | C2 | semidirect |
| 4. #14582922 | C2 | semidirect |
| 6. M16×Dic43 | C2 | semidirect |
| 17. Dic43⋊C8 | C22 | semidirect |
| 19. #13063235 | C22 | semidirect |
| 20. C8×Dic43 | C22 | semidirect |
| 67. C2×Dic43 | M16 | semidirect |
| 100. C43 | #2920 | semidirect |