Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
820 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D43 |
| commutator | C23×C43 | C24 |
| Frattini | C23 | C23×D43 |
| Fitting | C22×C4⋊C4×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C22×C4⋊C4 | D43 |
| hypocenter | C43 | C2×#397 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14582825 | C2 | direct (N × H) |
| 4. C2×C43⋊#95 | C2 | semidirect |
| 5. C2×C43⋊#95 | C2 | semidirect |
| 6. C22×C4⋊C4×C43 | C2 | semidirect |
| 14. C43⋊#95 | C22 | semidirect |
| 15. C43⋊#95 | C22 | semidirect |
| 19. C2×C4⋊C4×C43 | C22 | semidirect |
| 95. C2×C43 | #397 | semidirect |
| 102. C22×C4⋊C4 | D43 | semidirect |
| 108. C43 | C2×#397 | semidirect |
| 115. C2×C4⋊C4 | C2×D43 | semidirect |
| 197. C2 | #14582825 | direct (N × H) |