Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1232 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 189 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×#380 | C2 |
| hypercenter | #380 | D43 |
| hypocenter | C43 | #2408 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D172 | C2 | semidirect |
| 2. C2×#13063300 | C2 | semidirect |
| 3. C2×#13063295 | C2 | semidirect |
| 4. C2×C4×C22⋊D43 | C2 | semidirect |
| 5. #14582817 | C2 | semidirect |
| 6. #14582809 | C2 | semidirect |
| 7. #14582800 | C2 | semidirect |
| 8. #14582754 | C2 | semidirect |
| 9. C43×#380 | C2 | semidirect |
| 15. C22×D172 | C22 | semidirect |
| 17. C22×C4×D43 | C22 | semidirect |
| 21. C2×Dic43⋊C4 | C22 | semidirect |
| 23. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 24. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 25. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 26. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 27. C2×C4×Dic43 | C22 | semidirect |
| 29. C2×C4⋊C4×C43 | C22 | semidirect |
| 31. #95×C43 | C22 | semidirect |
| 41. C22×C4×C43 | D4 | semidirect |
| 47. C2×C22⋊D43 | D4 | semidirect |
| 59. C2×D172 | D4 | semidirect |
| 93. C22×D43 | C2×D4 | semidirect |
| 109. C2×Dic43 | C2×D4 | semidirect |
| 118. C22×C43 | #121 | semidirect |
| 139. C4×C43 | #120 | semidirect |
| 159. #380 | D43 | semidirect |
| 161. C43 | #2408 | semidirect |
| 175. C2×C4⋊C4 | C2×D43 | semidirect |
| 183. #95 | C2×D43 | semidirect |
| 210. C22×C4 | D172 | semidirect |
| 283. C22 | #13063300 | semidirect |
| 294. C4 | #13063295 | semidirect |