Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1728 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1728 conjugacy classes of subgroups — too many to draw. Only its 557 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 | C2×C4⋊Q8×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C2×C4⋊Q8 | D43 |
| hypocenter | C43 | C2×#532 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#10621902 | C2 | semidirect |
| 2. #14583450 | C2 | direct (N × H) |
| 3. C2×#13063322 | C2 | semidirect |
| 4. C2×#13063314 | C2 | semidirect |
| 5. C2×#13063300 | C2 | semidirect |
| 6. C2×#13063287 | C2 | semidirect |
| 7. C2×C42×D43 | C2 | semidirect |
| 8. C2×C4⋊Q8×C43 | C2 | semidirect |
| 10. C2×#10621902 | C22 | semidirect |
| 17. #13063322 | C22 | semidirect |
| 18. #13063314 | C22 | semidirect |
| 19. #13063300 | C22 | semidirect |
| 20. #13063287 | C22 | semidirect |
| 24. C42×D43 | C22 | semidirect |
| 26. C4⋊Q8×C43 | C22 | semidirect |
| 47. C2×C4×D43 | D4 | semidirect |
| 66. C2×C4×C43 | #41 | semidirect |
| 79. C4×D43 | C2×D4 | semidirect |
| 91. C4×C43 | C2×#41 | semidirect |
| 95. C2×C43 | #532 | semidirect |
| 102. C2×C4⋊Q8 | D43 | semidirect |
| 108. C43 | C2×#532 | semidirect |
| 118. C4⋊Q8 | C2×D43 | semidirect |
| 176. C2×C4 | #10621902 | semidirect |
| 193. C4 | C2×#10621902 | semidirect |
| 196. C2 | #14583450 | direct (N × H) |