Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #121×D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#473 | C2 |
| socle | C2×C43 | C2×#121 |
| hypercenter | #473 | D43 |
| hypocenter | C43 | #3067 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #473 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583698 | C2 | semidirect |
| 2. C2×#13063348 | C2 | semidirect |
| 3. #131×D43 | C2 | semidirect |
| 4. #14583171 | C2 | semidirect |
| 5. #14583170 | C2 | semidirect |
| 6. #14583169 | C2 | semidirect |
| 7. #14583165 | C2 | semidirect |
| 8. #14583164 | C2 | semidirect |
| 9. #108×D43 | C2 | semidirect |
| 10. #14582882 | C2 | semidirect |
| 11. C43×#473 | C2 | semidirect |
| 25. C2×#10621884 | C22 | semidirect |
| 26. C2×D344 | C22 | semidirect |
| 37. #13063261 | C22 | semidirect |
| 38. #13063260 | C22 | semidirect |
| 39. #13063244 | C22 | semidirect |
| 40. #13063241 | C22 | semidirect |
| 41. #13063241 | C22 | semidirect |
| 43. C2×Q16×C43 | C22 | semidirect |
| 45. #108×C43 | C22 | semidirect |
| 46. #101×C43 | C22 | semidirect |
| 171. #473 | D43 | semidirect |
| 178. C43 | #3067 | semidirect |
| 193. C2×Q16 | C2×D43 | semidirect |
| 209. #108 | C2×D43 | semidirect |
| 211. #101 | C2×D43 | semidirect |