Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1088 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D43 |
| commutator | C22×C43 | C23×C4 |
| Frattini | C23 | C23×D43 |
| Fitting | C2×#117×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C2×#117 | D43 |
| hypocenter | C43 | #2280 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13063284 | C2 | semidirect |
| 3. #14582760 | C2 | semidirect |
| 4. #14582756 | C2 | semidirect |
| 6. C4×(C2×D43)⋊C4 | C2 | semidirect |
| 7. C2×#117×C43 | C2 | semidirect |
| 12. C22×C4×D43 | C4 | semidirect |
| 16. C2×C4⋊Dic43 | C22 | semidirect |
| 19. C2×C4×Dic43 | C22 | semidirect |
| 20. C43⋊#95 | C22 | semidirect |
| 23. C2×C4⋊C4×C43 | C22 | semidirect |
| 25. C2×C42×C43 | C22 | semidirect |
| 73. C2×C4×C43 | C22⋊C4 | semidirect |
| 101. C2×D43 | #117 | semidirect |
| 116. C2×#117 | D43 | semidirect |
| 121. C43 | #2280 | semidirect |
| 133. C2×C4⋊C4 | C2×D43 | semidirect |
| 138. C2×C42 | C2×D43 | semidirect |
| 195. C2×C4 | (C2×D43)⋊C4 | semidirect |