Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13063298 |
| commutator | C2×C4×C43 | C22×C4 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#344 | C2 |
| socle | C2×C43 | #388 |
| hypercenter | #344 | D43 |
| hypocenter | C43 | #1932 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #344 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14582947 | C2 | semidirect |
| 5. M16×Dic43 | C2 | semidirect |
| 6. #14582658 | C2 | semidirect |
| 7. C43×#344 | C2 | semidirect |
| 16. #13063243 | C4 | semidirect |
| 17. #13063241 | C4 | semidirect |
| 101. #344 | D43 | semidirect |
| 103. C43 | #1932 | semidirect |