Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 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 | #2948 |
| 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. #14583373 | C2 | semidirect |
| 3. #14583012 | C2 | semidirect |
| 4. C4×D344 | C2 | semidirect |
| 5. #14582937 | C2 | semidirect |
| 6. #14582905 | C2 | semidirect |
| 7. C43×#405 | C2 | semidirect |
| 9. C2×D344 | C4 | semidirect |
| 12. C4×D172 | C22 | semidirect |
| 16. #13063259 | C22 | semidirect |
| 17. #13063257 | C22 | semidirect |
| 18. #13063247 | C22 | semidirect |
| 22. #97×C43 | C22 | semidirect |
| 23. C4×C8×C43 | C22 | semidirect |
| 28. C2×D172 | C2×C4 | semidirect |
| 32. C2×C8×C43 | C2×C4 | semidirect |
| 43. D344 | C2×C4 | semidirect |
| 44. D344 | C2×C4 | semidirect |
| 84. #405 | D43 | semidirect |
| 85. C43 | #2948 | semidirect |
| 100. #97 | C2×D43 | semidirect |
| 101. C4×C8 | C2×D43 | semidirect |
| 112. C2×C8 | C4×D43 | semidirect |