Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1160 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 269 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 | C22×C43 | C23×C4 |
| Fitting | C22×C22⋊C4×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C22×C22⋊C4 | D43 |
| hypocenter | C43 | #2308 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C22⋊Dic43 | C2 | semidirect |
| 3. #14582778 | C2 | semidirect |
| 4. #14582776 | C2 | semidirect |
| 5. #14582760 | C2 | semidirect |
| 6. #14582754 | C2 | semidirect |
| 7. C22×C22⋊C4×C43 | C2 | semidirect |
| 11. C22×C22⋊D43 | C4 | semidirect |
| 15. C23×Dic43 | C22 | semidirect |
| 18. C2×C22⋊Dic43 | C22 | semidirect |
| 19. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 20. C43⋊#95 | C22 | semidirect |
| 22. C23×C4×C43 | C22 | semidirect |
| 25. C2×C22⋊C4×C43 | C22 | semidirect |
| 36. C23×D43 | C2×C4 | semidirect |
| 46. C2×C22⋊D43 | C2×C4 | semidirect |
| 47. C2×C22⋊D43 | C2×C4 | semidirect |
| 52. C22×Dic43 | C2×C4 | semidirect |
| 66. C23×C43 | C22⋊C4 | semidirect |
| 133. C22×C22⋊C4 | D43 | semidirect |
| 138. C43 | #2308 | semidirect |
| 148. C23×C4 | C2×D43 | semidirect |
| 155. C2×C22⋊C4 | C2×D43 | semidirect |
| 205. C23 | (C2×D43)⋊C4 | semidirect |