Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D43 |
| commutator | C4×C43 | C22×C8 |
| Frattini | C42 | C22×D43 |
| Fitting | C43×D4⋊C8 | C2 |
| socle | C22×C43 | C2×C22⋊C4 |
| hypercenter | D4⋊C8 | D43 |
| hypocenter | C43 | #1478 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14582951 | C2 | semidirect |
| 3. #14582950 | C2 | semidirect |
| 4. #14582628 | C2 | semidirect |
| 5. D4⋊(C43⋊C8) | C2 | semidirect |
| 6. #14582626 | C2 | semidirect |
| 7. C43×D4⋊C8 | C2 | semidirect |
| 18. C4⋊(C43⋊C8) | C22 | semidirect |
| 22. C4×C43⋊C8 | C22 | semidirect |
| 25. C4⋊C8×C43 | C22 | semidirect |
| 26. C4×C8×C43 | C22 | semidirect |
| 33. D4×D43 | C8 | semidirect |
| 127. D4⋊C8 | D43 | semidirect |
| 128. C43 | #1478 | semidirect |
| 142. C4⋊C8 | C2×D43 | semidirect |
| 147. C4×C8 | C2×D43 | semidirect |