Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1476 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1476 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, Frattini | C22 | C24×D43 |
| commutator, socle | C22×C43 | C25 |
| Fitting | C4×#41×C43 | C2 |
| hypercenter | C4×#41 | D43 |
| hypocenter | C43 | #3499 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063372 | C2 | semidirect |
| 2. Q8×D172 | C2 | semidirect |
| 3. #14583553 | C2 | semidirect |
| 4. #14583475 | C2 | semidirect |
| 5. #14583449 | C2 | semidirect |
| 6. C2×#13063325 | C2 | semidirect |
| 7. C4×#41×C43 | C2 | semidirect |
| 28. #41×C43 | D4 | semidirect |
| 78. C4×C43 | 2−1+4 | semidirect |
| 91. C4×#41 | D43 | semidirect |
| 92. C43 | #3499 | semidirect |
| 115. #41 | D172 | semidirect |
| 164. C4 | #13063372 | semidirect |