Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
628 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C43×#392 | C2 |
| hypercenter | #392 | D43 |
| hypocenter | C43 | #2631 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063311 | C2 | semidirect |
| 2. C2×D4×Dic43 | C2 | semidirect |
| 3. #14582826 | C2 | semidirect |
| 4. #14582824 | C2 | semidirect |
| 5. #14582811 | C2 | semidirect |
| 6. #14582807 | C2 | semidirect |
| 7. #14582807 | C2 | semidirect |
| 8. #14582779 | C2 | semidirect |
| 9. #14582776 | C2 | semidirect |
| 10. #14582766 | C2 | semidirect |
| 11. C43×#392 | C2 | semidirect |
| 73. C4×Dic43 | D4 | semidirect |
| 164. #392 | D43 | semidirect |
| 168. C43 | #2631 | semidirect |