Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
824 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C22×C22⋊C4×C43 | C2 |
| hypercenter | C22×C22⋊C4 | D43 |
| hypocenter | C43 | #2617 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063299 | C2 | semidirect |
| 2. C2×#13063294 | C2 | semidirect |
| 3. #14582824 | C2 | semidirect |
| 4. #14582815 | C2 | semidirect |
| 5. #14582808 | C2 | semidirect |
| 6. #14582778 | C2 | semidirect |
| 7. #14582759 | C2 | semidirect |
| 8. C22×C22⋊C4×C43 | C2 | semidirect |
| 9. C22×D172 | C22 | semidirect |
| 14. C2×C4⋊Dic43 | C22 | semidirect |
| 15. C2×C4⋊Dic43 | C22 | semidirect |
| 18. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 19. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 20. C43⋊#95 | C22 | semidirect |
| 21. C43⋊#95 | C22 | semidirect |
| 32. C24×C43 | D4 | semidirect |
| 39. C22×C4×C43 | D4 | semidirect |
| 136. C22×C22⋊C4 | D43 | semidirect |
| 142. C43 | #2617 | semidirect |
| 167. C24 | D172 | semidirect |
| 183. C22×C4 | C22⋊D43 | semidirect |