Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
412 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊C4×D43 |
| commutator | C22×C43 | C2×C42 |
| Frattini | C24 | C22×D43 |
| Fitting | C43×#342 | C2 |
| socle | C22×C43 | C2×C22⋊C4 |
| hypercenter | #342 | D43 |
| hypocenter | C43 | C4×#99 |
| LCS | G ▷ C22×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ #342 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C22⋊C4×Dic43 | C2 | semidirect |
| 4. #14582666 | C2 | semidirect |
| 5. C43×#342 | C2 | semidirect |
| 8. C22×C4×D43 | C4 | semidirect |
| 11. C2×Dic43⋊C4 | C4 | semidirect |
| 13. C2×(C2×D43)⋊C4 | C4 | semidirect |
| 15. C2×C4×Dic43 | C4 | semidirect |
| 16. #13063239 | C4 | semidirect |
| 41. C22⋊C4×C43 | C2×C4 | semidirect |
| 43. C22⋊Dic43 | C2×C4 | semidirect |
| 60. C22×D43 | C42 | semidirect |
| 79. C2×Dic43 | C42 | semidirect |
| 109. Dic43 | #99 | semidirect |
| 123. #342 | D43 | semidirect |
| 124. C43 | C4×#99 | semidirect |
| 164. C22⋊C4 | C4×D43 | semidirect |