Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1348 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 213 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 | C4×C22⋊C4×C43 | C2 |
| hypercenter | C4×C22⋊C4 | D43 |
| hypocenter | C43 | #2433 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D172 | C2 | semidirect |
| 2. C2×#13063322 | C2 | semidirect |
| 3. C2×#13063299 | C2 | semidirect |
| 4. C2×#13063295 | C2 | semidirect |
| 5. #14582809 | C2 | semidirect |
| 6. #14582801 | C2 | semidirect |
| 7. C4×C22⋊C4×C43 | C2 | semidirect |
| 13. C22×D172 | C22 | semidirect |
| 14. C22×D172 | C22 | semidirect |
| 19. C2×C4⋊Dic43 | C22 | semidirect |
| 20. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 21. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 24. C2×C42×C43 | C22 | semidirect |
| 25. #95×C43 | C22 | semidirect |
| 34. C22×C4×C43 | D4 | semidirect |
| 51. C2×D172 | D4 | semidirect |
| 52. C22⋊C4×C43 | D4 | semidirect |
| 82. C2×C4×C43 | C2×D4 | semidirect |
| 93. C22×C43 | #127 | semidirect |
| 110. C4×C43 | #120 | semidirect |
| 126. C4×C22⋊C4 | D43 | semidirect |
| 127. C43 | #2433 | semidirect |
| 144. C2×C42 | C2×D43 | semidirect |
| 145. #95 | C2×D43 | semidirect |
| 168. C22×C4 | D172 | semidirect |
| 175. C22⋊C4 | D172 | semidirect |
| 208. C2×C4 | C2×D172 | semidirect |
| 223. C22 | #13063322 | semidirect |
| 231. C4 | #13063295 | semidirect |