Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1620 conjugacy classes of subgroups; only the 573 normal subgroups are shown.
This group has 1620 conjugacy classes of subgroups — too many to draw. Only its 573 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D43 |
| commutator | C22×C43 | C25 |
| Frattini | C22 | C24×D43 |
| Fitting | C22×#41×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C22×#41 | D43 |
| hypocenter | C43 | C2×#548 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q8×D43 | C2 | semidirect |
| 2. #14583556 | C2 | direct (N × H) |
| 3. C2×#13063312 | C2 | semidirect |
| 4. C2×#13063304 | C2 | semidirect |
| 5. C2×#13063296 | C2 | semidirect |
| 6. C2×Q8×Dic43 | C2 | semidirect |
| 7. C2×C4×C22⋊D43 | C2 | semidirect |
| 8. C22×#41×C43 | C2 | semidirect |
| 11. C2×Q8×D43 | C22 | semidirect |
| 14. #13063312 | C22 | semidirect |
| 15. #13063304 | C22 | semidirect |
| 16. #13063296 | C22 | semidirect |
| 17. Q8×Dic43 | C22 | semidirect |
| 18. C4×C22⋊D43 | C22 | semidirect |
| 26. C2×#41×C43 | C22 | semidirect |
| 33. C2×Q8×C43 | D4 | semidirect |
| 64. C22×D43 | #41 | semidirect |
| 66. Q8×C43 | C2×D4 | semidirect |
| 93. C2×D43 | C2×#41 | semidirect |
| 101. C2×C43 | #548 | semidirect |
| 106. C22×#41 | D43 | semidirect |
| 114. C43 | C2×#548 | semidirect |
| 116. C2×#41 | C2×D43 | semidirect |
| 142. C2×Q8 | C22⋊D43 | semidirect |
| 173. Q8 | C2×C22⋊D43 | semidirect |
| 207. C2 | #14583556 | direct (N × H) |