Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 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 | C22 | C22×D172 |
| commutator | C4×C43 | C23×C4 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#405 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #405 | D43 |
| hypocenter | C43 | #2949 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14583376 | C2 | semidirect |
| 4. #14583001 | C2 | semidirect |
| 5. C4×#10621873 | C2 | semidirect |
| 6. #14582937 | C2 | semidirect |
| 7. #14582909 | C2 | semidirect |
| 9. C43×#405 | C2 | semidirect |
| 12. C2×#10621873 | C4 | semidirect |
| 15. C4×Dic86 | C22 | semidirect |
| 23. #13063259 | C22 | semidirect |
| 24. #13063257 | C22 | semidirect |
| 25. #13063250 | C22 | semidirect |
| 30. #97×C43 | C22 | semidirect |
| 31. C4×C8×C43 | C22 | semidirect |
| 42. C2×Dic86 | C2×C4 | semidirect |
| 45. C2×C8×C43 | C2×C4 | semidirect |
| 61. #10621873 | C2×C4 | semidirect |
| 62. #10621873 | C2×C4 | semidirect |
| 112. #405 | D43 | semidirect |
| 113. C43 | #2949 | semidirect |
| 134. #97 | C2×D43 | semidirect |
| 135. C4×C8 | C2×D43 | semidirect |
| 151. C2×C8 | C4×D43 | semidirect |