Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1640 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1640 conjugacy classes of subgroups — too many to draw. Only its 565 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×C4⋊C4×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C22×C4⋊C4 | D43 |
| hypocenter | C43 | C2×#537 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#10621898 | C2 | semidirect |
| 2. #14583480 | C2 | direct (N × H) |
| 3. C2×#13063305 | C2 | semidirect |
| 4. C2×#13063300 | C2 | semidirect |
| 5. C2×#13063299 | C2 | semidirect |
| 6. C22×C4⋊C4×C43 | C2 | semidirect |
| 8. C2×#10621898 | C22 | semidirect |
| 14. #13063305 | C22 | semidirect |
| 15. #13063300 | C22 | semidirect |
| 16. #13063299 | C22 | semidirect |
| 22. C2×C4⋊C4×C43 | C22 | semidirect |
| 26. C22×C4×C43 | D4 | semidirect |
| 58. C2×C4×C43 | C2×D4 | semidirect |
| 85. C2×C43 | #537 | semidirect |
| 95. C22×C4⋊C4 | D43 | semidirect |
| 96. C43 | C2×#537 | semidirect |
| 111. C2×C4⋊C4 | C2×D43 | semidirect |
| 128. C22×C4 | D172 | semidirect |
| 155. C2×C4 | C2×D172 | semidirect |
| 175. C2 | #14583480 | direct (N × H) |