Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
816 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 141 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 | C43×#399 | C2 |
| hypercenter | #399 | D43 |
| hypocenter | C43 | #2668 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #399 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063300 | C2 | semidirect |
| 2. C2×#13063295 | C2 | semidirect |
| 3. #14582825 | C2 | semidirect |
| 4. #14582816 | C2 | semidirect |
| 5. #14582808 | C2 | semidirect |
| 6. #14582777 | C2 | semidirect |
| 7. #14582775 | C2 | semidirect |
| 8. #14582754 | C2 | semidirect |
| 9. C43×#399 | C2 | semidirect |
| 13. C22×D172 | C22 | semidirect |
| 15. C22×C4×D43 | C22 | semidirect |
| 23. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 24. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 25. C43⋊#95 | C22 | semidirect |
| 26. C43⋊#95 | C22 | semidirect |
| 27. C43⋊#95 | C22 | semidirect |
| 28. C2×C4⋊C4×C43 | C22 | semidirect |
| 29. C2×C4⋊C4×C43 | C22 | semidirect |
| 32. #95×C43 | C22 | semidirect |
| 57. C2×D172 | D4 | semidirect |
| 160. #399 | D43 | semidirect |
| 167. C43 | #2668 | semidirect |
| 176. C2×C4⋊C4 | C2×D43 | semidirect |
| 177. C2×C4⋊C4 | C2×D43 | semidirect |
| 190. #95 | C2×D43 | semidirect |